Decay of heat semigroups in \(L^\infty\) and applications to nonlinear parabolic problems in unbounded domains

DOI10.1006/jfan.2000.3554zbMath0954.35032OpenAlexW2054834024MaRDI QIDQ1572901

Philippe Souplet

Publication date: 5 February 2001

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jfan.2000.3554

zbMATH Keywords

Poincaré inequalityheat semigroup

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60) Stability in context of PDEs (35B35) One-parameter semigroups and linear evolution equations (47D06) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items (11)

Asymptotic behavior and attractors for reaction diffusion equations in unbounded domains ⋮ Bi-space global attractors for a class of nonclassical parabolic equations with arbitrary polynomial growth in unbounded domain ⋮ The closed range property for the \(\overline{\partial}\)-operator on planar domains ⋮ Analysis of the viscous Cahn-Hilliard equation in \(\mathbb R^N\) ⋮ Morrey spaces and classification of global solutions for a supercritical semilinear heat equation in \(\mathbb{R}^n\) ⋮ On the stability of equilibria to weakly coupled parabolic systems in unbounded domains ⋮ Stable Equilibria to Parabolic Systems in Unbounded Domains ⋮ Existence and nonexistence of global classical solutions to porous medium and plasma equations with singular sources ⋮ Numerical verification for existence of a global-in-time solution to semilinear parabolic equations ⋮ Maximum principles for weak solutions of degenerate elliptic equations with a uniformly elliptic direction ⋮ Positive solutions of elliptic and parabolic equations with convex-concave nonlinearities

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the asymptotic behaviour of solutions of nonlinear parabolic equations
• On the lowest eigenvalue of the Laplacian for the intersection of two domains
• Gaussian bounds for the Dirichlet heat kernel
• On solutions of initial -boundary problem for \(u_t=u_{xx}+1/(1-u)\)
• A note on Hayman's theorem on the bass note of a drum
• Stability properties of parabolic equations in unbounded domains
• A short note on quenching phenomena for semilinear parabolic equations
• Quenching for Semilinear Singular Parabolic Problems
• Some bounds for principal frequency
• Decay of mass for a semilinear parabolic equation
• Geometry of unbounded domains,poincaré inequalities and stability in semilinear parabolic equations
• On the asymptotics of solutions of parabolic equations on unbounded domains
• The principal eigenvalue and maximum principle for second‐order elliptic operators in general domains
• Decay of global solutions, stability and blowup for a reaction-diffusion problem with free boundary
• On the alexandroff‐bakelman‐pucci estimate and the reversed hölder inequality for solutions of elliptic and parabolic equations
• On kernels, eigenvalues, and eigenfunctions of operators related to elliptic problems
• On the growth of solutions of quasi‐linear parabolic equations

This page was built for publication: Decay of heat semigroups in \(L^\infty\) and applications to nonlinear parabolic problems in unbounded domains