A positivity property of solutions of nonlinear diffusion equations

DOI10.1016/0022-0396(84)90024-XzbMath0488.35041MaRDI QIDQ1166019

Michiel Bertsch, Lambertus A. Peletier

Publication date: 1984

Published in: Journal of Differential Equations (Search for Journal in Brave)

zbMATH Keywords

nonnegative solution

Mathematics Subject Classification ID

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)

Related Items (13)

On a class of nonlinear Neumann problems of parabolic type: Blow-up of solutions ⋮ On a degenerate diffusion equation of the form \(c(z)_ t=\phi (z_ x)_ x\) with application to population dynamics ⋮ Asymptotic spherical symmetry of the free boundary in degenerate diffusion equations ⋮ Positivity versus localization in degenerate diffusion equations ⋮ Approaching critical decay in a strongly degenerate parabolic equation ⋮ The porous medium equation: The superslow diffusion case ⋮ A comparison principle for the porous media equation with absorption ⋮ On a Degenerate Nonlocal Parabolic Problem Describing Infinite Dimensional Replicator Dynamics ⋮ Regularity of the interfaces with sign changes of solutions of the one-dimensional porous medium equation ⋮ When are the spatial level surfaces of solutions of diffusion equations invariant with respect to the time variable? ⋮ A necessary and sufficient condition for global existence for a degenerate parabolic boundary value problem ⋮ Degenerate diffusion and the Stefan problem ⋮ The principle of linearized stability of a class of degenerate diffusion equations

Cites Work

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• The asymptotic profile of solutions of degenerate diffusion equations
• Large time behaviour of solutions of the porous medium equation in bounded domains
• Regularizing effects for \(u_ t\) + A phi(u) = 0 in \(L^ 1\).
• On the diffusion of biological populations
• The Behavior of the Support of Solutions of the Equation of Nonlinear Heat Conduction with Absorption in One Dimension
• Stabilization of solutions of a degenerate nonlinear diffusion problem
• Decay of solutions of a degenerate nonlinear diffusion equation
• Regularizing Effects for u t = Δϕ(u)

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