Any large solution of a non-linear heat conduction equation becomes monotonic in time

DOI10.1017/S0308210500028857zbMath0741.35004MaRDI QIDQ3974214

S. A. Posashkov, Victor A. Galaktionov

Publication date: 25 June 1992

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/44304

zbMATH Keywords

Cauchy problembounded sufficiently smooth initial functionmethod of intersection comparisonquasilinear uniformly parabolic equation

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear parabolic equations (35K55) Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05)

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Necessary and sufficient conditions for complete blow-up and extinction for one-dimensional quasilinear heat equations, Geometrical properties of the solutions of one-dimensional nonlinear parabolic equations, Asymptotics of blowup for weakly quasilinear parabolic problems, Blow-up behaviour for nonlinearly perturbed semilinear parabolic equations, Total versus single point blow-up for a nonlocal gaseous ignition model, Incomplete blow-up and singular interfaces for quasilinear heat equations, Monotonicity in time of large solutions to a nonlinear heat equation

Cites Work

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• On the total variation of solutions of parabolic equations
• The zero set of a solution of a parabolic equation.
• Analyticity at the boundary of solutions of nonlinear second-order parabolic equations
• Analyticity up to the boundary of solutions of nonlinear parabolic equations