Existence results for nonlinear parabolic equations via strong convergence of truncations

DOI10.1007/BF02505907zbMath0957.35066MaRDI QIDQ1570429

Alessio Porretta

Publication date: 16 March 2001

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

zbMATH Keywords

truncation methodsign condition\(L^1\)-initial datapseudomonotone operator of Leray-Lions type

Mathematics Subject Classification ID

Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60) Theoretical approximation in context of PDEs (35A35)

Related Items

Existence results for a class of nonlinear parabolic equations of generalized porous medium type with measure data, Existence of renormalized solutions to a nonlinear parabolic boundary value problem with a singular lower order term and a nonhomogeneous datum, Existence result of entropy solution for some nonlinear parabolic problems under natural growths in Musielak spaces, Potential Estimates and Quasilinear Parabolic Equations with Measure Data, An \(L^1\)-theory for a nonlinear temporal periodic problem involving \(p(x)\)-growth structure with a strong dependence on gradients, Existence of solutions for a class of nonlinear elliptic problems with measure data in the setting of Musielak-Orlicz-Sobolev spaces, Existence and regularity results for some nonlinear singular parabolic problems with absorption terms, Weak and Renormalized Solutions to a Hypoelliptic Mean Field Games System, Strong convergence of weighted gradients in parabolic equations and applications to global generalized solvability of cross-diffusive systems, On Some Nonlinear Elliptic Problems with Large Monotonocity in Musielak–Orlicz–Sobolev Spaces, Solvability of Strongly Nonlinear Obstacle Parabolic Problems in Inhomogeneous Orlicz–Sobolev Spaces, Nonlinear parabolic problem with/without an explosive condition on the boundary, Quasilinear class of noncoercive parabolic problems with Hardy potential and L1-data, On the existence and regularity of solutions to singular parabolic \(p\)-Laplacian equations with absorption term, Generalized parabolic problems having a gradient term with natural growth and a measure initial data, Some results on the existence of weak periodic solutions for quasilinear parabolic systems with L1 data, Existence of a renormalized solution of nonlinear parabolic equations with general measure data, Stability and existence results for a class of nonlinear parabolic equations with three lower order terms and measure data using Lorentz spaces, Unnamed Item, Existence and uniqueness of a renormalized solution for a fairly general class of nonlinear parabolic problems, Existence of renormalized solutions to quasilinear elliptic problems with general measure data, Existence of renomalized solution for nonlinear elliptic boundary value problem without \(\Delta_2\)-condition, Stability/nonstability properties of renormalized/entropy solutions for degenerate parabolic equations with \(L^1\)/measure data, Renormalized solutions of nonlinear parabolic equations with diffuse measure data, Regularizing effect for some parabolic problems with perturbed terms and irregular data, Existence of renormalized solutions for strongly nonlinear parabolic problems with measure data, Renormalized and entropy solutions for nonlinear parabolic equations with variable exponents and \(L^{1}\) data, Renormalized solutions to a reaction-diffusion system applied to image denoising, Existence of renormalized solutions to a nonlinear parabolic equation in L¹ setting with nonstandard growth condition and gradient term, Unnamed Item, Existence and uniqueness result for a class of nonlinear parabolic equations with L¹data, Entropy solutions for nonlinear unilateral parabolic inequalities in Orlicz–Sobolev spaces, Existence result for a class of doubly nonlinear parabolic systems, The extinction versus the blow-up: global and non-global existence of solutions of source types of degenerate parabolic equations with a singular absorption, Strongly nonlinear elliptic problem with measure data in Musielak-Orlicz spaces, Parabolic equations with nonlinear singularities, Pointwise gradient estimates in multi-dimensional slow diffusion equations with a singular quenching term, On some \(\overrightarrow{p(x)}\) anisotropic elliptic equations in unbounded domain, Asymptotic behavior of solutions for linear parabolic equations with general measure data, On the weak theory for mean field games systems, Unnamed Item, Existence results for a Cauchy-Dirichlet parabolic problem with a repulsive gradient term, A Time-Dependent Optimal Harvesting Problem with Measure-Valued Solutions, Nonlinear evolution equations with noncoercive lower order terms, Unnamed Item, Diffuse measures and nonlinear parabolic equations, On the notion of renormalized solution to nonlinear parabolic equations with general measure data, Renormalized solutions to a class of noncoercive parabolic equations with variable exponents, Generalized solutions for a class of nonlinear parabolic problems with irregular data in unbounded domains, Asymptotic behavior of solutions for nonlinear parabolic operators with natural growth term and measure data, Strongly nonlinear parabolic inequality in Orlicz spaces via a sequence of penalized equations, Mean field games with congestion, Existence and uniqueness of a solution for a class of parabolic equations with two unbounded nonlinearities, Global attractors for the \(p\)-Laplacian equations with nonregular data, Local estimates for parabolic equations with nonlinear gradient terms, \(L^\infty \) estimates and uniqueness results for nonlinear parabolic equations with gradient absorption terms, On some class of nonlinear parabolic inequalities in Orlicz spaces, Existence of solutions for a class of porous medium type equations with \(L^1\) data, On degenerate parabolic equations, Perturbation effects for some nonlinear parabolic equations with lower order term and \(L^1\)-data, Unnamed Item, Existence of solutions of cancer invasion parabolic system with integrable data, Periodic solutions to parabolic equation with singular \(p\)-Laplacian, Asymptotic behavior result for obstacle parabolic problems with measure data, Existence of a solution for a class of parabolic equations with three unbounded nonlinearities, natural growth terms and \(L^1\) data, Quasi-linear diffusion equations with gradient terms and \(L^{1}\) data., Unnamed Item, Entropy solutions for nonlinear parabolic equations with nonstandard growth in non-reflexive Orlicz spaces, Renormalized solutions of nonlinear parabolic equations with general measure data, Large solutions for nonlinear parabolic equations without absorption terms, On certain mathematical models in continuum thermomechanics, Existence of solutions for some doubly degenerate parabolic equations with natural growth terms, Existence and uniqueness of renormalized periodic solution to a nonlinear parabolic problem with variable exponent and \(L^1\) data, Parabolic inequalities in \(L^{1}\) as limits of renormalized equations, Existence results for a non-linear obstacle parabolic semicoercive problems with lower order term, Approximation of diffuse measures for parabolic capacities, On some new non-linear diffusion models for the image filtering, Renormalized and entropy solutions for the fractional \(p\)-Laplacian evolution equations, Weak solutions to Fokker-Planck equations and mean field games, Quasi-linear diffusion equations with gradient terms and \(L^1\) data, Unnamed Item, A one-dimensional nonlinear heat equation with a singular term, Unnamed Item, Stefan problems with nonlinear diffusion and convection, Existence and uniqueness of a renormalized solution for nonlinear degenerate parabolic equations with diffuse measure data, Renormalized solutions to nonlinear parabolic problems with blowing up coefficients and general measure data, Renormalized solutions for a nonlinear parabolic equation with variable exponents and \(L^{1}\)-data, Existence and uniqueness of renormalized solutions to nonlinear parabolic equations with lower order term and diffuse measure data, On the planning problem for the mean field games system, On the study of strongly parabolic problems involving anisotropic operators in \(L^1\), Renormalized solutions for nonlinear elliptic equations with variable exponents and \(L^1\) data, Existence results of renormalized solutions for nonlinear \(p(\cdot)\)-parabolic equations with possibly singular measure data, On some parabolic equations involving superlinear singular gradient terms, Stability properties for quasilinear parabolic equations with measure data, Existence results for doubly nonlinear parabolic equations with two lower-order terms and \(L^1\)-data, Unnamed Item, Nonlinear parabolic equations with soft measure data, On the coupling between a Navier-Stokes equation and a total energy equation in spatial dimension \(N=3\), Unnamed Item, Renormalized solution for a nonlinear parabolic problems with noncoercivity in divergence form in Musielak-Orlicz spaces, Comparison results for unbounded solutions for a parabolic Cauchy-Dirichlet problem with superlinear gradient growth, On some regularity results of parabolic problems with nonlinear perturbed terms and general data, Entropy and renormalized solutions to the general nonlinear elliptic equations in Musielak-Orlicz spaces, Global Existence for Nonlinear Parabolic Problems With Measure Data– Applications to Non-uniqueness for Parabolic Problems With Critical Gradient terms, Large time behavior of solutions to parabolic equations with Dirichlet operators and nonlinear dependence on measure data, On initial boundary value problems with equivalued surface for nonlinear parabolic equations, Existence and uniqueness of entropy solutions to nonlinear parabolic problem with homogeneous Dirichlet boundary conditions involving variable exponent, Energy and large time estimates for nonlinear porous medium flow with nonlocal pressure in \(\mathbb{R}^N\), Complete quenching phenomenon and instantaneous shrinking of support of solutions of degenerate parabolic equations with nonlinear singular absorption, Unnamed Item, Unnamed Item, Unnamed Item, Unnamed Item, Existence result to a parabolic equation with quadratic gradient term and an \(L^1\) source, A probabilistic representation of the solution of some quasi-linear PDE with a divergence form operator. Application to existence of weak solutions of FBSDE., Existence and uniqueness of bounded weak solutions for some nonlinear parabolic problems, Asymptotic behavior for nonlinear degenerate parabolic equations with irregular data, Some results on a singular parabolic equation in one dimension case, Existence and uniqueness of renormalized solutions for initial boundary value parabolic problems with possibly very singular right-hand side, Entropy solutions for a nonlinear parabolic problems with lower order term in Orlicz spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the Cauchy problem for Boltzmann equations: Global existence and weak stability
• Nonlinear elliptic and parabolic equations involving measure data
• Compact sets in the space \(L^ p(0,T;B)\)
• Existence of bounded solutions for non linear elliptic unilateral problems
• Nonlinear parabolic equations with measure data
• Regularity for entropy solutions of parabolic \(p\)-Laplacian type equations
• On parabolic initial-boundary value problems with critical growth for the gradient
• Existence and uniqueness of “entropy” solutions of parabolic problems with L1 data
• On the existence of weak solutions for quasilinear parabolic initial-boundary value problems
• Strongly nonlinear elliptic equations having natural growth terms and L1 data
• Existence and uniqueness for a degenerate parabolic equation with 𝐿¹-data
• Entropy solutions for nonlinear elliptic equations in L1
• Truncations and monotonicity methods for parabolic equations
• Renormalised solutions of nonlinear parabolic problems with L¹ data: existence and uniqueness
• Nonlinear parabolic equations with natural growth conditions and L1 data