scientific article
From MaRDI portal
Publication:3961188
zbMath0496.35011MaRDI QIDQ3961188
Publication date: 1982
Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.
pattern formationsemilinear parabolic equationlap-numbercomplexity of the graph of a solutionhighly oscillating perturbation
Asymptotic behavior of solutions to PDEs (35B40) Nonlinear parabolic equations (35K55) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Perturbations in context of PDEs (35B20)
Related Items
Semilinear Neumann boundary value problems on a rectangle ⋮ Existence and regularity theorems for a two-phase degenerate stefan problem with convection ⋮ Spatial Critical Points of Solutions of a One-Dimensional Nonlinear Parabolic Problem ⋮ Numbers of zeros on invariant manifolds in reaction- diffusion equations ⋮ On the quenching behavior of the solution of a semilinear parabolic equation ⋮ Convergence in general periodic parabolic equations in one space dimension ⋮ Convergence to a traveling wave in the lgarithmic diffusion equation with a bistable nonlinearity ⋮ Continuity properties on \(p\) for \(p\)-Laplacian parabolic problems ⋮ Localization of solutions of a nonlinear fokker–planck equation with dirichlet boundary conditions ⋮ A non-autonomous bifurcation problem for a non-local scalar one-dimensional parabolic equation ⋮ On the sign-variations of solutions of nonlinear two-point boundary value problems ⋮ Blow-up sets for a complex-valued semilinear heat equation ⋮ Existence and properties of ancient solutions of the Yamabe flow ⋮ Nonuniqueness of nematic liquid crystal flows in dimension three ⋮ Existence of multi-dimensional pulsating fronts for KPP equations: a new formulation approach ⋮ Lifting properties of minimal sets for parabolic equations on 𝑆¹ with reflection symmetry ⋮ Nonexistence of radial time-periodic solutions of reaction-diffusion equations with generic nonlinearities ⋮ Sturm attractors for fully nonlinear parabolic equations ⋮ Morse decompositions for delay-difference equations ⋮ The well-posedness of a free boundary problem for Burgers' equation ⋮ Spreading and Extinction of Solutions to the Logarithmic Diffusion Equation with a Logistic Reaction ⋮ Multiplicative controllability for nonlinear degenerate parabolic equations between sign-changing states ⋮ Probability bounds for reflecting diffusion processes ⋮ Meanders, zero numbers and the cell structure of Sturm global attractors ⋮ Braided connecting orbits in parabolic equations via computational homology ⋮ Phase portrait control for 1D monostable and bistable reaction–diffusion equations ⋮ Long-time asymptotics of the zero level set for the heat equation ⋮ Realization of period maps of planar Hamiltonian systems ⋮ Potential comparison and asymptotics in scalar conservation laws without convexity ⋮ Global dynamics of blow-up profiles in one-dimensional reaction diffusion equations ⋮ Connectivity and design of planar global attractors of Sturm type. II: Connection graphs ⋮ Asymptotic behavior of zeros of solutions for parabolic equations ⋮ The number of stationary solutions for a one-dimensional Budyko-type climate model ⋮ Extinction behaviour for fast diffusion equations with absorption ⋮ On the affine heat equation for non-convex curves ⋮ Bifurcations in a parabolic equation with variable diffusion ⋮ A Free Boundary Focusing Problem ⋮ The maximum principle for control systems described by linear parabolic equations ⋮ The Dynamics of Rotating Waves in Scalar Reaction Diffusion Equations ⋮ Using Aleksandrov reflection to estimate the location of the center of expansion ⋮ Generic hyperbolicity of equilibria and periodic orbits of the parabolic equation on the circle ⋮ How parabolic free boundaries approximate hyperbolic fronts ⋮ Traveling wave solutions of harmonic heat flow ⋮ Sign changing periodic solutions for the Chafee–Infante equation ⋮ Regularity of the interfaces with sign changes of solutions of the one-dimensional porous medium equation ⋮ On Minimal Sets of Scalar Parabolic Equations with Skew-Product Structures ⋮ Connectivity and design of planar global attractors of Sturm type. III: Small and platonic examples ⋮ On a free boundary problem for the curvature flow with driving force ⋮ Orbit equivalence of global attractors of semilinear parabolic differential equations ⋮ Scalar parabolic PDEs and braids ⋮ Asymptotic Behavior of the interfaces to a nonlinear degenerate diffusion equation in population dynamics ⋮ Unbounded Sturm Global Attractors for Semilinear Parabolic Equations on the Circle ⋮ Discrete Ljapunov functionals and $\omega $-limit sets ⋮ A non-autonomous scalar one-dimensional dissipative parabolic problem: the description of the dynamics ⋮ Structure and bifurcation of pullback attractors in a non-autonomous Chafee-Infante equation ⋮ Equivalence between radial solutions of different parabolic gradient-diffusion equations and applications ⋮ Uniqueness of solutions of mean field equations in 𝑅² ⋮ Behavior of the gradient for solutions of parabolic equations on the circle ⋮ On the Two‐Dimensional Muskat Problem with Monotone Large Initial Data ⋮ The viscous Cahn-Hilliard equation: Morse decomposition and structure of the global attractor ⋮ On the dynamics of a degenerate parabolic equation: global bifurcation of stationary states and convergence ⋮ Equilibration of unit mass solutions to a degenerate parabolic equation with a nonlocal gradient nonlinearity ⋮ Multiple spreading phenomena for a free boundary problem of a reaction-diffusion equation with a certain class of bistable nonlinearity ⋮ The impact of finite precision arithmetic and sensitivity on the numerical solution of partial differential equations ⋮ Schoenflies spheres as boundaries of bounded unstable manifolds in gradient Sturm systems ⋮ Heteroclinic orbits between rotating waves of semilinear parabolic equations on the circle ⋮ Monotone solutions to quasilinear parabolic equations ⋮ On stabilization of solutions to boundary value problems for quasilinear parabolic equations periodic in time ⋮ Long-time behavior of almost periodically forced parabolic equations on the circle ⋮ Bifurcation and stability of stationary solutions of nonlocal scalar reaction-diffusion equations ⋮ Necessary and sufficient conditions for complete blow-up and extinction for one-dimensional quasilinear heat equations ⋮ Floquet bundles for scalar parabolic equations ⋮ \(L^1\)-stability of periodic stationary solutions of scalar convection-diffusion equations ⋮ Non-periodicity in chemostat equations: a multi-dimensional negative Bendixson-Dulac criterion ⋮ Gradient-like structure and Morse decompositions for time-periodic one- dimensional parabolic equations ⋮ Asymptotics in the critical case for Whitham type equations ⋮ Structure of \(\omega\)-limit sets for almost-periodic parabolic equations on \(S^{1}\) with reflection symmetry ⋮ Unbounded solutions to autonomous quasilinear parabolic equations ⋮ Morse decompositions for delay-differential equations ⋮ Mean curvature flow through singularities for surfaces of rotation ⋮ Blow-up rates of solutions of initial-boundary value problems for a quasi-linear parabolic equation ⋮ Existence of type II blowup solutions for a semilinear heat equation with critical nonlinearity ⋮ Geometrical properties of the solutions of one-dimensional nonlinear parabolic equations ⋮ Order structures and the heat equation ⋮ Infinite time blow-up of solutions to a nonlinear parabolic problem ⋮ Sturm 3-ball global attractors 3: examples of Thom-Smale complexes ⋮ Lap number properties for \(p\)-Laplacian problems investigated by Lyapunov methods ⋮ The periodic orbits of an area preserving twist map ⋮ Almost automorphically-forced flows on \(S^1\) or \(\mathbb{R}\) in one-dimensional almost periodic semilinear heat equations ⋮ Ergodicity of minimal sets in scalar parabolic equations ⋮ Multiplicative controllability for semilinear reaction-diffusion equations with finitely many changes of sign ⋮ On the shape of the solutions of second order parabolic partial differential equations ⋮ Convergence in time-periodic quasilinear parabolic equations in one space dimension ⋮ Sturm attractors for quasilinear parabolic equations ⋮ Behavior of solutions to nonlinear parabolic equations at large time ⋮ Nonlinear heat conduction through an externally heated radiant plasma: Background analysis for a numerical study ⋮ Critical exponent for the bipolar blowup in a semilinear parabolic equation ⋮ Characterization of non-autonomous attractors of a perturbed infinite-dimensional gradient system ⋮ On some aspects of a nonlinear convection-diffusion equation arising in heat-induced moisture transport in porous media ⋮ Generic Morse-Smale property for the parabolic equation on the circle ⋮ On the nonexistence of finite time bubble trees in symmetric harmonic map heat flows from the disk to the 2-sphere. ⋮ Qualitative behavior of solutions for thermodynamically consistent Stefan problems with surface tension ⋮ Multiple blow-up for a porous medium equation with reaction ⋮ A quasilinar heat equation with a source: Peaking, localization, symmetry exact solutions, asymptotics, structures ⋮ Almost automorphically and almost periodically forced circle flows of almost periodic parabolic equations on \(S^1\) ⋮ A Poincaré-Bendixson theorem for scalar reaction diffusion equations ⋮ Behaviour of solutions of a singular diffusion equation near the extinction time. ⋮ A permutation characterization of Sturm global attractors of Hamiltonian type ⋮ Sets of unique continuation for heat equation ⋮ Multiple nodal solutions having shared componentwise nodal numbers for coupled Schrödinger equations ⋮ Nonlinear Sturm global attractors: unstable manifold decompositions as regular CW-complexes ⋮ Quasiconvergence in parabolic equations in one space dimension ⋮ On the regularity of weak solutions of a one-dimensional two-phase degenerate Stefan problem with convection ⋮ Transversality in scalar reaction-diffusion equations on a circle ⋮ The role of critical exponents in blow-up theorems: The sequel ⋮ An extension of Zeeman's notion of structural stability to non-invertible maps ⋮ Stability of stationary solutions of a one-dimensional parabolic equation with homogeneous Neumann boundary conditions ⋮ Properties of the attractor of a scalar parabolic PDE ⋮ Stability of steady states for one dimensional parabolic equations with nonlinear boundary conditions ⋮ Reaction-diffusion systems coupled at the boundary and the Morse-Smale property ⋮ Global bifurcation diagrams of one node solutions in a class of degenerate boundary value problems ⋮ Topological instabilities in families of semilinear parabolic problems subject to nonlinear perturbations ⋮ Corrections to: ``Nodal properties of solutions of parabolic equations ⋮ A sequence of order relations: Encoding heteroclinic connections in scalar parabolic PDE ⋮ Long time behavior of solutions for a scalar nonlocal reaction-diffusion equation ⋮ The zero number diminishing property under general boundary conditions ⋮ Regularity results for a one-dimensional two-phase degenerate Stefan problem ⋮ Explicit construction of an inertial manifold for a reaction diffusion equation ⋮ Convergence, asymptotic periodicity, and finite-point blow-up in one- dimensional semilinear heat equations ⋮ Asymptotic behavior of solutions to the logarithmic diffusion equation with a linear source ⋮ Sturm 3-ball global attractors. 1: Thom-Smale complexes and meanders ⋮ Blow-up and regularization rates, loss and recovery of boundary conditions for the superquadratic viscous Hamilton-Jacobi equation ⋮ Grow-up for a quasilinear heat equation with a localized reaction in higher dimensions ⋮ Global branches of non-radially symmetric solutions to a semilinear Neumann problem in a disk ⋮ Radial solutions and phase separation in a system of two coupled Schrödinger equations ⋮ Traveling wave solutions of the heat flow of director fields ⋮ Non-wandering points for autonomous/periodic parabolic equations on the circle ⋮ Asymptotic shape of cusp singularities in curve shortening ⋮ Sturm attractors for quasilinear parabolic equations with singular coefficients ⋮ A Liouville theorem for the viscous Burgers's equation ⋮ Critical exponents for the blowup of solutions with sign changes in a semilinear parabolic equation. II ⋮ Slow decay of solutions in a semilinear dissipative parabolic equation ⋮ Blow-up of sign-changing solutions for a one-dimensional nonlinear diffusion equation ⋮ Slow-motion manifolds, dormant instability, and singular perturbations ⋮ Sturm 3-ball global attractors 2: design of Thom-Smale complexes ⋮ Two-phase entropy solutions of a forward-backward parabolic equation ⋮ Realization of meander permutations by boundary value problems ⋮ Boundary orders and geometry of the signed Thom-Smale complex for Sturm global attractors ⋮ Asymptotic behavior of the isoperimetric deficit for expanding convex plane curves ⋮ Asymptotic behaviour and source-type solutions for a diffusion-convection equation ⋮ Simplicity of zeros in scalar parabolic equations ⋮ Some infinite-dimensional Morse-Smale systems defined by parabolic partial differential equations ⋮ Nodal properties of solutions of parabolic equations ⋮ Stable patterns for fourth-order parabolic equations ⋮ Uniqueness and stability of regional blow-up in a porous-medium equation ⋮ On the total - and strict total - positivity of the kernels associated with parabolic initial boundary value problems ⋮ Ergodic attractors and almost-everywhere asymptotics of scalar semilinear parabolic differential equations ⋮ The Morse-Smale property for a semilinear parabolic equation ⋮ Vanishing latent heat limit in a Stefan-like problem arising in biology. ⋮ A dynamical system for a nonlocal parabolic equation with exponential nonlinearity
