Localization and blow up of thermal waves in nonlinear heat conduction with peaking

DOI10.1007/BF01456972zbMath0627.35048OpenAlexW2071483975MaRDI QIDQ1092329

Brian H. Gilding, Miguel Angel Herrero

Publication date: 1988

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/164458

zbMATH Keywords

initial-boundary value problemblow-upfree boundarylocalizationporous media equationthermal wavenonlinear heat conductionnonnegative generalized solution

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear parabolic equations (35K55) Flows in porous media; filtration; seepage (76S05) Degenerate parabolic equations (35K65) Partial differential equations of mathematical physics and other areas of application (35Q99)

Related Items (10)

Critical Fujita exponents for degenerate parabolic equations coupled via nonlinear boundary flux ⋮ Asymptotic behaviour in time of KdV type equations with time dependent coefficients ⋮ On the blow-up set for non-Newtonian equation with a nonlinear boundary condition ⋮ A nonlocal nonlinear diffusion equation with blowing up boundary conditions ⋮ Limiting profile of solutions of quasilinear parabolic equations with flat peaking ⋮ The balance between nonlinear inwards and outwards boundary flux for a nonlinear heat equation ⋮ The role of nonlinear diffusion in non-simultaneous blow-up ⋮ Localized blow-up regimes for quasilinear doubly degenerate parabolic equations ⋮ Blow-up set for the non-Newtonian polytropic filtration equation subjected to nonlinear Neumann boundary condition ⋮ Blowing up boundary conditions for a nonlocal nonlinear diffusion equation in several space dimensions

Cites Work

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• On a class of similarity solutions of the porous media equation. III
• On a class of similarity solutions of the porous media equation
• Intersections of solutions of nonlinear parabolic equations
• On a class of similarity solutions of the porous media equation. II
• METHODS OF CONSTRUCTING APPROXIMATE SELF-SIMILAR SOLUTIONS OF NONLINEAR HEAT EQUATIONS. I
• Continuity of the Density of a Gas Flow in a Porous Medium
• Stabilization of Flows Through Porous Media

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