Extinction for a quasilinear heat equation with absorprtion i. technique of intersection comparison

DOI10.1080/03605309408821046zbMath0831.35073OpenAlexW2010603837MaRDI QIDQ4304236

Juan Luis Vazquez, Victor A. Galaktionov

Publication date: 10 October 1994

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605309408821046

zbMATH Keywords

radially symmetric solutionsstrong absorptionslow diffusionlap numberdead core problemssingle point extinction

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Initial value problems for second-order parabolic equations (35K15)

Related Items (27)

Extinction for a singular diffusion equation with strong gradient absorption revisited ⋮ Long-time behavior of solutions to a class of parabolic equations with nonstandard growth condition ⋮ Geometrical properties of the solutions of one-dimensional nonlinear parabolic equations ⋮ Singular standing-ring solutions of nonlinear partial differential equations ⋮ Extinction for a quasilinear heat equation with absorption ii. a dynamical systems approach ⋮ A necessary condition for the instantaneous shrinking property of solutions to a semilinear heat equation ⋮ Extinction of solutions to a diffusion problem with nonlinear sources and variable density ⋮ Extinction and focusing behaviour of spherical and annular flames described by a free boundary problem ⋮ Bifurcations of self-similar solutions for reversing interfaces in the slow diffusion equation with strong absorption ⋮ Interface behaviour of the slow diffusion equation with strong absorption: Intermediate-asymptotic properties ⋮ Properties of solutions to porous medium problems with different sources and boundary conditions ⋮ Invariant sets and solutions to the two-dimensional nonlinear reaction-diffusion equations ⋮ Exact solutions of nonlinear diffusion-convection-reaction equation: a Lie symmetry analysis approach ⋮ Extinction for a fast diffusion equation with a nonlinear nonlocal source ⋮ Critical extinction exponents for a fast diffusion equation with nonlocal source and absorption ⋮ Extinction and non-extinction for a polytropic filtration equation with a nonlocal source ⋮ Extinction behaviour for fast diffusion equations with absorption ⋮ Nonhomogeneous initial-boundary value problems for nonlinear diffusion-convection equations ⋮ Dead-core rates for the fast diffusion equation with a spatially dependent strong absorption ⋮ Extinction of solutions to a class of fast diffusion systems with nonlinear sources ⋮ Dynamical systems of inequalities and nonlinear parabolic equations ⋮ On some nonlinear problems in mathematical physics with exponents close to critical ones ⋮ Extinction and non-extinction for a polytropic filtration system with non-linear sources ⋮ Dead-core rate for the fast diffusion equation with strong absorption in higher dimensional cases ⋮ EXTINCTION AND NON-EXTINCTION OF SOLUTIONS TO A P-LAPLACE EQUATION WITH A NONLOCAL SOURCE AND AN ABSORPTION TERM ⋮ Critical exponents and lower bounds of blow-up rate for a reaction-diffusion system ⋮ Nonexistence of global solutions for quasilinear backward parabolic inequalities with \(p\)-Laplace-type operator

Cites Work

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• Nonlinear Heat Conduction with Absorption: Space Localization and Extinction in Finite Time
• The One-Dimensional Nonlinear Heat Equation with Absorption: Regularity of Solutions and Interfaces
• The zero set of a solution of a parabolic equation.
• Best Possible Upper Bound for Blowup Solutions of the Quasilinear Heat Conduction Equation with Source
• The propagation of disturbances in problems of non-linear heat conduction with absorption
• Gestaltaussagen über Lösungen parabolischer Differentialgleichungen.

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