Source-type solutions of degenerate diffusion equations with absorption
type: Item
instance of: scholarly article
title: Source-type solutions of degenerate diffusion equations with absorption
zbMATH Open document ID: 0581.35035
DOI: 10.1007/BF02761403
published in: Israel Journal of Mathematics
publication date: 1985-01-01T00:00:00Z
review text: This paper proves a sharp existence theorem for the problem \(u_ t=\Delta (u^ m)-u^ p\), \(m>1\), with initial data a Dirac delta function. The paper also presents some interesting results on the convergence of the solution to the initial data, as \(t\downarrow 0\).
reviewed by: Michael Sever
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35K15
Mathematics Subject Classification ID: 35A05
Mathematics Subject Classification ID: 35R05
zbMATH DE Number: 3929545
zbMATH Keywords: source-type solutions
zbMATH Keywords: absorption
zbMATH Keywords: degenerate diffusion equations
zbMATH Keywords: existence
zbMATH Keywords: initial data
author: S. Kamin
author: Lambertus A. Peletier
MaRDI profile type: Publication
cites work: Stabilization of solutions of a degenerate nonlinear diffusion problem
cites work: Q5817208
cites work: Positivity versus localization in degenerate diffusion equations
cites work: Nonlinear parabolic equations involving measures as initial conditions
cites work: A very singular solution of the heat equation with absorption
cites work: Q3041629
cites work: Large time behavior of the solutions of a semilinear parabolic equation in \(\mathbb R^ n\)
cites work: The propagation of disturbances in problems of non-linear heat conduction with absorption
cites work: Q3732141
cites work: DIFFUSION FROM AN INSTANTANEOUS POINT SOURCE WITH A CONCENTRATION-DEPENDENT COEFFICIENT
cites work: Q3962703
cites work: Uniqueness of the solutions of ut−Δϕ(u) = 0 with initial datum a measure
description: scientific article; zbMATH DE number 3929545