Well-posedness of the Dirichlet problem for the non-linear diffusion equation in non-smooth domains

DOI10.1090/S0002-9947-04-03464-6zbMath1074.35052OpenAlexW2106469757MaRDI QIDQ4819753

Ugur G. Abdulla

Publication date: 5 October 2004

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

Full work available at URL: https://doi.org/10.1090/s0002-9947-04-03464-6

zbMATH Keywords

Dirichlet problemuniquenesscomparison theoremsnonlinear diffusionnonsmooth domainscontinuous dependenceporous equation

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60)

Related Items (10)

Evolution of interfaces for the nonlinear parabolic p-Laplacian-type reaction-diffusion equations. II. Fast diffusion vs. absorption ⋮ Evolution of interfaces for the non-linear parabolic p-Laplacian type reaction–diffusion equations ⋮ Continuity up to the boundary for obstacle problems to porous medium type equations ⋮ Interface development for the nonlinear degenerate multidimensional reaction-diffusion equations. II: Fast diffusion versus absorption ⋮ An existence result for evolution equations in non-cylindrical domains ⋮ Reaction-diffusion in nonsmooth and closed domains ⋮ Evolution of interfaces for the nonlinear double degenerate parabolic equation of turbulent filtration with absorption ⋮ Boundary regularity for the porous medium equation ⋮ Nonlinear theory for thermoelastic solids with mass diffusion ⋮ Interface development for the nonlinear degenerate multidimensional reaction-diffusion equations

Cites Work

• Classes of solutions of linear systems of partial differential equations of parabolic type
• Large time behaviour of solutions of the porous medium equation in bounded domains
• Quasilinear elliptic-parabolic differential equations
• Continuity of weak solutions to certain singular parabolic equations
• Reaction-diffusion in a closed domain formed by irregular curves
• Reaction-diffusion in irregular domains
• Evolution of interfaces and explicit asymptotics at infinity for the fast diffusion equation with absorption
• Continuity of the Density of a Gas Flow in a Porous Medium
• First Boundary Value Problem for the Diffusion Equation I. Iterated Logarithm Test for the Boundary Regularity and Solvability
• Interface Development and Local Solutions to Reaction-Diffusion Equations
• Interior and Boundary Continuity of Weak Solutions of Degenerate Parabolic Equations
• Continuity of solutions of a singular parabolic equation
• On the Dirichlet problem for the nonlinear diffusion equation in non-smooth domains
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