scientific article
From MaRDI portal
Publication:3886160
DOI10.1512/iumj.1980.29.29007zbMath0443.35034OpenAlexW4253709798MaRDI QIDQ3886160
Publication date: 1980
Published in: Indiana University Mathematics Journal (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1512/iumj.1980.29.29007
Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Nonlinear parabolic equations (35K55) Stability in context of PDEs (35B35) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Qualitative properties of solutions to partial differential equations (35B99)
Related Items
Besov-Morrey spaces: Function space theory and applications to non-linear PDE, A Threshold Result for a Non-local Parabolic Equation, NON-UNIQUENESS FOR A CRITICAL NON-LINEAR HEAT EQUATION, APPROXIMATION OF BLOWING UP SOLUTIONS TO SEMILINEAR PARABOLIC EQUATIONS USING "MASS CONTROLLED" PARABOLIC SYSTEMS, Partial Regularity in Time for the Space-Homogeneous Landau equation with Coulomb Potential, On the blow-up of solutions of a convective reaction diffusion equation, Semilinear heat equations and the navier-stokes equation with distributions in new function spaces as initial data, A note on strong instability of standing waves for some semilinear wave and heat equations, Blow-up of nonnegative solutions of an abstract semilinear heat equation with convex source, Solvability of a semilinear heat equation on Riemannian manifolds, New life-span results for the nonlinear heat equation, Fractional Cauchy problem with memory effects, Global well posedness for the semilinear edge-degenerate parabolic equations on singular manifolds, Global existence and spatial analyticity for a nonlocal flux with fractional diffusion, Convergence analysis of the splitting method to the nonlinear heat equation, Global existence and convergence results for a class of nonlinear time fractional diffusion equation, The global solution and blowup of a spatiotemporal EIT problem with a dynamical boundary condition, Local L^p-solution for semilinear heat equation with fractional noise, Semilinear parabolic equations in Herz spaces, Life span bounds for reaction-diffusion equation with a space-time integral source term, Blow-Up vs. Global Existence for a Fujita-Type Heat Exchanger System, Nonlinear partial differential equations on noncommutative Euclidean spaces, Initial traces and solvability for a semilinear heat equation on a half space of ℝ^{ℕ}, Global existence and finite-time blow-up for a nonlinear nonlocal evolution equation, Quasi self-similarity and its application to the global in time solvability of a superlinear heat equation, Solvability for time‐fractional semilinear parabolic equations with singular initial data, Existence of sign-changing solutions for the Hénon type parabolic equation with singular initial data, Blowup and ill-posedness for the complex, periodic KdV equation, Non-linear heat equation on the hyperbolic space: global existence and finite-time blow-up, Qualitative Properties of Solutions of Degenerate Parabolic Equations via Energy Approaches, Distribution-valued initial data for the complex ginzburg-landau equation, Unnamed Item, Unnamed Item, Solvability of a Semilinear Heat Equation via a Quasi Scale Invariance, On an instantaneous blow-up of solutions of evolutionary problems on the half-line, Blow-up in a class of non-linear parabolic problems with time-dependent coefficients under Robin type boundary conditions, Local and global existence for evolution p-Laplacian equation with time-dependent source, Nonglobal existence of solutions for a generalized Ginzburg-Landau equation coupled with a Poisson equation, Nonlinear diffusion equations on unbounded fractal domains, NON WELL POSEDNESS OF PARABOLIC EQUATIONS WITH SUPERCRITICAL NONLINEARITIES, Exact controllability to trajectories for semilinear heat equations with discontinuous diffusion coefficients, Unnamed Item, Global existence, asymptotic behavior and self-similar solutions for a class of semilinear parabolic systems, The Cauchy problem for critical and subcritical semilinear parabolic equations in \(L^r\). I, On a free boundary problem for the curvature flow with driving force, Instantaneous blow-up versus local solubility of the Cauchy problem for a two-dimensional equation of a semiconductor with heating, Semilinear parabolic equations involving measures and low regularity data, No LocalL1Solution for a Nonlinear Heat Equation, Global Solution for a Stochastic Ginzburg-Landau Equation with Multiplicative Noise, Strongly anisotropic type II blow up at an isolated point, On the Stability of Type I Blow Up For the Energy Super Critical Heat Equation, Initial-boundary value problems for a reaction-diffusion equation, Unnamed Item, Below-threshold solutions of a focusing energy-critical heat equation in ℝ⁴, The Cauchy problem for a system of nonlinear heat equations in two space dimensions, On the critical exponent “instantaneous blow-up” versus “local solubility” in the Cauchy problem for a model equation of Sobolev type, Remarks on the critical nonlinear high-order heat equation, Stability analysis in order-preserving systems in the presence of symmetry, Geometry of unbounded domains,poincaré inequalities and stability in semilinear parabolic equations, Isometric decomposition operators, function spaces \(E_{p,q}^{\lambda}\) and applications to nonlinear evolution equations, A bound for global solutions of semilinear heat equations, Supersolutions for a class of semilinear heat equations, On the quenching of a nonlocal parabolic problem arising in electrostatic MEMS control, Critère d'existence de solutions positives pour des équations semi- linéaires non monotones. (Existence condition of positive solutions of non-monotonic semilinear equations), Weak and strong solutions of the complex Ginzburg-Landau equation, Regularity properties of mild solutions for a class of Volterra equations with critical nonlinearities, Blow-up analysis for a reaction-diffusion equation with weighted nonlocal inner absorptions under nonlinear boundary flux, Periodicity and ergodicity for abstract evolution equations with critical nonlinearities, Hardy inequalities and dynamic instability of singular Yamabe metrics, Blowup and blowup time for a class of semilinear pseudo-parabolic equations with high initial energy, Existence and nonexistence of global solutions for a semilinear reaction-diffusion system, The heat equation with singular nonlinearity and singular initial data, Error estimates for semidiscrete Galerkin type approximations to semilinear evolution equations with nonsmooth initial data, Asymptotic behavior and decay estimates of the solutions for a nonlinear parabolic equation with exponential nonlinearity, Complete blow-up after \(T_{\max}\) for the solution of a semilinear heat equation, Existence of solutions for a fractional semilinear parabolic equation with singular initial data, A complete characterisation of local existence for semilinear heat equations in Lebesgue spaces, Self-similar subsolutions and blowup for nonlinear parabolic equations, A note on the inhomogeneous nonlinear heat equation in two space dimensions, Singularity and blow-up estimates via Liouville-type theorems for Hardy-Hénon parabolic equations, Analytic solutions of some nonlinear diffusion equations, Instantaneous blow-up versus local solvability for one problem of propagation of nonlinear waves in semiconductors, Cauchy problem for nonlinear parabolic equations with a gradient term, On a semilinear parabolic equation with inverse-square potential, Non-existence of local solutions of semilinear heat equations of Osgood type in bounded domains, Blow-up analysis for a semilinear parabolic equation with time-dependent coefficients under nonlinear boundary flux, Global existence for a delay differential equations, Blow-up phenomena for a system of semilinear heat equations with nonlinear boundary flux, Local and global existence for quasilinear parabolic systems with a strongly nonlinear source, Global existence and non-existence for a higher-order parabolic equation with time-fractional term, The Navier-Stokes initial value problem in \(L^ p\)., Semilinear evolution transmission problems across fractal layers, Universal bounds for global solutions of a diffusion equation with a nonlocal reaction term., Global, decaying solutions of a focusing energy-critical heat equation in \(\mathbb{R}^4\), On the growth of mass for a viscous Hamilton-Jacobi equation, Convergence of minimax structures and continuation of critical points for singularly perturbed systems, Blow-up phenomena for a semilinear heat equation with nonlinear boundary condition. I., The local theory for viscous Hamilton--Jacobi equations in Lebesgue spaces., On well-posedness of semilinear parabolic and elliptic problems in the hyperbolic space, A quasilinar heat equation with a source: Peaking, localization, symmetry exact solutions, asymptotics, structures, A note on well-posedness of semilinear reaction-diffusion problem with singular initial data, Global existence and blow-up phenomena for nonlinear divergence form parabolic equations with inhomogeneous Neumann boundary conditions, Existence and non-existence of global solutions for a semilinear heat equation, Longtime behavior of semilinear reaction-diffusion equations on the whole space, Nonuniqueness for a critical nonlinear heat equation with any initial data., Existence of nodal solutions of semilinear equations in \({\mathbb{R}}^ n\), Some existence and nonexistence theorems for solutions of degenerate parabolic equations, Semilinear evolution problems with Ventcel-type conditions on fractal boundaries, Initial blow-up rates and universal bounds for nonlinear heat equations., Boundedness and blow up for a semilinear reaction-diffusion system, Blowup for the nonlinear heat equation with small initial data in scale-invariant Besov norms, Cauchy problem for doubly degenerate parabolic equation with gradient source, Global existence and blow-up phenomena for \(p\)-Laplacian heat equation with inhomogeneous Neumann boundary conditions, Critical exponent for the global existence of solutions to a semilinear heat equation with degenerate coefficients, Energy non-collapsing and refined blowup for a semilinear heat equation, Remarks on the Cauchy problem for the one-dimensional quadratic (fractional) heat equation, Global existence, nonexistence and asymptotic behavior of solutions for the Cauchy problem of semilinear heat equations, Stability of ODE blow-up for the energy critical semilinear heat equation, Asymptotics for a class of heat equations with inhomogeneous nonlinearity, A priori bounds for superlinear elliptic equations with semidefinite nonlinearity, Linear higher order parabolic problems in locally uniform Lebesgue's spaces, Well-posedness, global existence and large time behavior for Hardy-Hénon parabolic equations, The heat equaton with general periodic boundary conditions, On blow-up and dynamics near ground states for some semilinear equations, Blow-up in \(p\)-Laplacian heat equations with nonlinear boundary conditions, Dynamics near the ground state for the energy critical nonlinear heat equation in large dimensions, Nonexistence of solutions to parabolic differential inequalities with a potential on Riemannian manifolds, Asymptotics for a class of coupled fractional heat equations, Non-autonomous parabolic problems with singular initial data in weighted spaces, Navier-Stokes equations and nonlinear heat equations in modulation spaces with negative derivative indices, On well-posedness of the semilinear heat equation on the sphere, Stability for semilinear parabolic equations with decaying potentials in \(\mathbb{R}^n\) and dynamical approach to the existence of ground states, New results on the Cauchy problem for parabolic systems and equations with strongly nonlinear sources, Attractors for non-autonomous parabolic problems with singular initial data, The Cauchy problem for heat equations with exponential nonlinearity, Exact controllability to trajectories for a semilinear heat equation with a superlinear nonlinearity, On the instantaneous blow-up of solutions of some quasilinear evolution problems, The role of forward self-similar solutions in the Cauchy problem for semilinear heat equations, A singular parabolic equation with logarithmic nonlinearity and \(L^p\)-initial data, Blow-up phenomena for a semilinear heat equation with nonlinear boundary condition. II., Convergence, asymptotic periodicity, and finite-point blow-up in one- dimensional semilinear heat equations, The evolution to localized and front solutions in a non-Lipschitz reaction-diffusion Cauchy problem with trivial initial data, A nonlinear equation in Banach spaces and applications to the well-posedness of Cauchy problems, A class of semilinear parabolic equations with singular initial data, Global existence and blowup for sign-changing solutions of the nonlinear heat equation, On global solutions and blow-up for Kuramoto-Sivashinsky-type models, and well-posed Burnett equations, Space-time means and solutions to a class of nonlinear parabolic equations, Fractal Burgers equations, Single point blow-up for a semilinear initial value problem, Well-posedness of a semilinear heat equation with weak initial data, Decay of heat semigroups in \(L^\infty\) and applications to nonlinear parabolic problems in unbounded domains, A remark on the energy blow-up behavior for nonlinear heat equations, On the absence of local solutions of several evolutionary problems, Dual semigroups and second order linear elliptic boundary value problems, Scaling in nonlinear parabolic equations, Parabolic problems with nonlinear boundary conditions and critical nonlinearities, On the asymptotic behavior of solutions of certain quasilinear parabolic equations, Solutions for semilinear parabolic equations in \(L^ p\) and regularity of weak solutions of the Navier-Stokes system, Existence, non-existence, and uniqueness for a heat equation with exponential nonlinearity in \(\mathbb R^2\), Local existence for evolution equations with nonlocal term in time and singular initial data, Asymptotic behavior and attractors for reaction diffusion equations in unbounded domains, Global in time solvability for a semilinear heat equation without the self-similar structure, Instantaneous blow-up for nonlinear Sobolev type equations with potentials on Riemannian manifolds, Well-posedness and regularity of the generalized Burgers equation in periodic Gevrey spaces, Composition operators on Herz-type Triebel-Lizorkin spaces with application to semilinear parabolic equations, Cauchy problem and initial traces for fast diffusion equation with space-dependent source, On the stability or instability of the singular solution of the semilinear heat equation with exponential reaction term, Critical blowup and global existence numbers for a weakly coupled system of reaction-diffusion equations, Fractional semilinear heat equations with singular and nondecaying initial data, Heat equation with an exponential nonlinear boundary condition in the half space, Sufficient conditions and bounds estimate of blow-up time for a fourth order parabolic equation, Local existence and nonexistence for fractional in time reaction-diffusion equations and systems with rapidly growing nonlinear terms, Optimal well-posedness and forward self-similar solution for the Hardy-Hénon parabolic equation in critical weighted Lebesgue spaces, Existence of solutions to some degenerate parabolic equation associated with the \(p\)-Laplacian in the critical case, Joint space-time analyticity of mild solutions to the Navier-Stokes equations, Existence of solutions with moving singularities for a semilinear heat equation with a critical exponent, On the well-posedness of the anisotropically-reduced two-dimensional Kuramoto-Sivashinsky equation, L∞-estimates of solutions of some nonlinear degenerate parabolic equations, Local existence and nonexistence for fractional in time weakly coupled reaction-diffusion systems, Time-dependent singularities in semilinear parabolic equations: existence of solutions, On the Cauchy Problem for Reaction-Diffusion Equations, Global and non global solutions for a class of coupled parabolic systems, A nonlinear heat equation with singular initial data, The Cauchy problem in local spaces for the complex Ginzburg-Landau equation. I: Compactness methods, Dynamical boundary problem for Dirichlet-to-Neumann operator with critical Sobolev exponent and Hardy potential, The cauchy problem for the critical nonlinear Schrödinger equation in Hs, Well-posedness of semilinear heat equations in \(L^1\), The Cauchy problem for heat equation with fractional Laplacian and exponential nonlinearity, Blow-up phenomena for a semilinear parabolic equation with weighted inner absorption under nonlinear boundary flux, Finite time blow up and non-uniform bound for solutions to a degenerate drift-diffusion equation with the mass critical exponent under non-weight condition, Critical dissipative estimate for a heat semigroup with a quadratic singular potential and critical exponent for nonlinear heat equations, Existence of solutions for an inhomogeneous fractional semilinear heat equation, Global positive solution to a semi-linear parabolic equation with potential on Riemannian manifold, Existence of solutions for a higher-order semilinear parabolic equation with singular initial data, Well-posedness for Hardy-Hénon parabolic equations with fractional Brownian noise, Local existence of solutions to some degenerate parabolic equation associated with the \(p\)-Laplacian, Singular Behavior in Nonlinear Parabolic Equations, A nonlinear fractional diffusion equation: well-posedness, comparison results, and blow-up, Local existence and non-existence for a fractional reaction-diffusion equation in Lebesgue spaces, Global existence to a reaction–diffusion equation through a self‐similar‐like upper solution, High initial energy finite time blowup with upper bound of blowup time of solution to semilinear parabolic equations, Local well-posedness for semilinear heat equations on H type groups, Bounds for Blow-Up Time in Nonlinear Parabolic Systems Under Various Boundary Conditions, On the numerical computation of blowing-up solutions for semilinear parabolic equations, GLOBAL SOLUTION AND BLOWUP OF SEMILINEAR HEAT EQUATION WITH CRITICAL SOBOLEV EXPONENT, \(L^{\infty }\) and decay estimates for higher-order semilinear diffusion-absorption equations, Iterative approximation of solutions for semilinear parabolic equations system, A semilinear heat equation with initial data in negative Sobolev spaces, Finite-time blowup for a complex Ginzburg-Landau equation with linear driving, Blow-up phenomena of solutions for a reaction-diffusion equation with weighted exponential nonlinearity, Blow-up time for nonlinear heat equations with transcendental nonlinearity, Asymptotically self-similar global solutions for a higher-order semilinear parabolic equation, ASYMPTOTIC SELF-SIMILAR BEHAVIOR OF SOLUTIONS FOR A SEMILINEAR PARABOLIC SYSTEM, Blowup stability of solutions of the nonlinear heat equation with a large life span, A characteristic of local existence for nonlinear fractional heat equations in Lebesgue spaces, On higher-order semilinear parabolic equations with measures as initial data, Large deviations and Gallavotti-Cohen principle for dissipative PDEs with rough noise, Non-unicité des solutions d'une équation d'évolution non-linéaire, A doubly critical semilinear heat equation in the \(L^1\) space, Optimal condition for blow-up of the critical \(L^q\) norm for the semilinear heat equation, Existence and nonexistence of solutions for the heat equation with a superlinear source term, Weakly coupled reaction-diffusion systems with rapidly growing nonlinearities and singular initial data, Behaviour of heat kernels of Schrödinger operators and applications to certain semilinear parabolic equations, Composition estimates and well-posedness for Hardy-Hénon parabolic equations in Besov spaces, Non-uniqueness for an energy-critical heat equation on \({\mathbb{R}}^2\), Existence of solutions to the slow diffusion equation with a nonlinear source, On the local existence for a weakly parabolic system in Lebesgue spaces, Coefficient stability of the solution of a difference scheme approximating a mixed problem for a semilinear parabolic equation, Type II blow-up mechanisms in a semilinear heat equation with critical Joseph-Lundgren exponent, Unnamed Item, Dynamic properties of the \(p\)-Laplacian reaction-diffusion equation in multi-dimensional space, Blow-up for a semilinear heat equation with Fujita's critical exponent on locally finite graphs, Self-similarity in the singularity formation for the unsteady Prandtl's equations and related problems, Existence and non-existence of global solutions for semilinear heat equations and inequalities on sub-Riemannian manifolds, and Fujita exponent on unimodular Lie groups, On the role of the Besov spaces for the solutions of the generalized Burgers equation in homogeneous Sobolev spaces, Unnamed Item, Uniqueness and non-uniqueness of solutions for critical Hardy-Hénon parabolic equations, Asymptotic analysis of an ordinary differential equation and non-uniqueness for a semilinear partial differential equation, SMALL GLOBAL SOLUTIONS FOR NONLINEAR COMPLEX GINZBURG–LANDAU EQUATIONS AND NONLINEAR DISSIPATIVE WAVE EQUATIONS IN SOBOLEV SPACES, Strong solutions of forward-backward stochastic differential equations with measurable coefficients, Local existence and nonexistence for reaction-diffusion systems with coupled exponential nonlinearities, On the Cauchy problem for the equation \(u'-\Delta u=u| u| ^{\gamma -1}\) in the supercritical case, Local well-posedness and finite time blow-up of solutions to an attraction-repulsion chemotaxis system in higher dimensions, Blow-up phenomena in parabolic problems with time dependent coefficients under Dirichlet boundary conditions, On the local existence for Hardy parabolic equations with singular initial data, Global existence and blow-up phenomena for divergence form parabolic equation with time-dependent coefficient in multidimensional space, On singularity formation for the two-dimensional unsteady Prandtl system around the axis, Local conditional regularity for the Landau equation with Coulomb potential, Compactness and single-point blowup of positive solutions on bounded domains, Non-uniqueness for a critical heat equation in two dimensions with singular data, A degenerate diffusion equation with a nonlinear source term, Nonautonomous semilinear Wentzell problems in fractal domains, The reaction-diffusion equation with Lewis function and critical Sobolev exponent, The nonlinear heat equation with high order mixed derivatives of the Dirac delta as initial values, Existence of global solution for reaction-diffusion systems with density dependent diffusion, Solvability of superlinear fractional parabolic equations, Self-similar large time behavior of solutions to Korteweg–de Vries–Burgers equation, The Cauchy problem for critical and subcritical semilinear parabolic equations in \(L^r\). II: Initial data in critical Sobolev spaces \(\dot{H}^{-s,r^s}\), A solution of the complex Ginzburg-Landau equation with a continuum of decay rates