Extinction and positivity for a doubly nonlinear degenerate parabolic equation

DOI10.1007/s10114-007-0944-6zbMath1128.35061OpenAlexW2164790140MaRDI QIDQ2465530

Xiaojing Xu, Hongjun Yuan, Chunling Cao, Song Zhe Lian, Wen-jie Gao

Publication date: 4 January 2008

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-007-0944-6

zbMATH Keywords

evolution equationpositivityextinctionhomogeneous Dirichlet conditiondoubly degenerate equation

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Initial-boundary value problems for second-order parabolic equations (35K20) Degenerate parabolic equations (35K65) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05)

Related Items (14)

The well-posedness of the solutions based on the \(L^1\) initial value condition ⋮ The global solution of a diffusion equation with nonlinear gradient term ⋮ Solution to nonlinear parabolic equations related to \(P\)-Laplacian ⋮ Qualitative properties of nonnegative solutions for a doubly nonlinear problem with variable exponents ⋮ Blow-up for doubly degenerate nonlinear parabolic equations ⋮ Extinction and decay estimates of solutions for a non-Newton polytropic filtration system ⋮ Infiltration equation with degeneracy on the boundary ⋮ The stability of the solutions of an anisotropic diffusion equation ⋮ Extinction and decay estimates of solutions for a class of doubly degenerate equations ⋮ On the stability of a non-Newtonian polytropic filtration equation ⋮ The partial boundary value condition for a polytropic filtration equation with variable exponents ⋮ The viscosity solutions of a nonlinear equation related to the \(p\)-Laplacian ⋮ Unnamed Item ⋮ On a weak solution matching up with the double degenerate parabolic equation

Cites Work

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• Hölder estimates for quasilinear doubly degenerate parabolic equations
• Large time behaviour of solutions of the porous medium equation in bounded domains
• The Cauchy problem for an equation in the theory of infiltration
• Homogeneous diffusion in \({\mathbb{R}}\) with power-like nonlinear diffusivity
• On doubly degenerate quasilinear parabolic equations of higher order
• On the equation of turbulent filtration in one- dimensional porous media
• Lipschitz continuity of the free boundary of some nonlinear degenerate parabolic equations

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