On boundedness of solutions of reaction-diffusion equations with nonlinear boundary conditions

DOI10.1090/S0002-9939-07-08980-0zbMath1173.35552MaRDI QIDQ5429436

José M. Arrieta

Publication date: 30 November 2007

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

blow-upnonlinear boundary conditionsbounded solutionslocal boundedness at the boundary

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60) Reaction-diffusion equations (35K57)

Related Items

Bifurcation in a reaction-diffusion model with nonlocal delay effect and nonlinear boundary condition ⋮ Controlled boundary explosions: dynamics after blow-up for some semilinear problems with global controls ⋮ Asymptotic regularity and attractors of the reaction-diffusion equation with nonlinear boundary condition ⋮ On the heat equation with nonlinearity and singular anisotropic potential on the boundary ⋮ Attractors of the non-autonomous reaction-diffusion equation with nonlinear boundary condition ⋮ Existence and multiplicity of self-similar solutions for heat equations with nonlinear boundary conditions

Cites Work

• Unnamed Item
• Complete blow-up after \(T_{\max}\) for the solution of a semilinear heat equation
• Parabolic problems with nonlinear boundary conditions and critical nonlinearities
• The problem of blow-up in nonlinear parabolic equations
• Porous medium equation with absorption and a nonlinear boundary condition
• On second-order effects in the boundary behaviour of large solutions of semilinear elliptic problems.
• Uniqueness and asymptotic behaviour for solutions of semilinear problems with boundary blow-up
• Localization on the Boundary of Blow-up for Reaction–Diffusion Equations with Nonlinear Boundary Conditions
• Continuation of blowup solutions of nonlinear heat equations in several space dimensions
• ON UNIQUENESS FOR THE INVERSE SCATTERING PROBLEM AT FIXED ENERGY FOR A METRIC ON
• Attractors of parabolic problems with nonlinear boundary conditions. uniform bounds
• Nonlinear balance for reaction-diffusion equations under nonlinear boundary conditions: Dissipativity and blow-up
• The influence of domain geometry in boundary blow-up elliptic problems.