Fundamental solutions and asymptotic behaviour for the p-Laplacian equations
type: Item
instance of: scholarly article
title: Fundamental solutions and asymptotic behaviour for the p-Laplacian equations
zbMATH Open document ID: 0699.35158
DOI: 10.4171/RMI/77
author: S. Kamin
author: Juan Luis Vázquez
published in: Revista Matemática Iberoamericana
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/39371
review text: We establish the uniqueness of fundamental solutions to the p-Laplacian equation \[ (PLE)\quad u_ t=div(| Du|^{p-2}Du),\quad p>2, \] defined for \(x\in {\mathbb{R}}^ N\), \(0<t<T\). We derive from this result the asymptotic behaviour of nonnegative solutions with finite mass, i.e. such that u(,t)\(\in L^ 1({\mathbb{R}}^ N)\). Our methods also apply to the porous medium equation \[ (PME)\quad u_ t=\Delta (u^ m),\quad m>1, \] giving new and simpler proofs of known results. We finally introduce yet another method of proving asymptotic results based on the idea of asymptotic radial symmetry. This method can be useful in dealing with more general equations.
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 76S05
Mathematics Subject Classification ID: 35A08
zbMATH DE Number: 4146630
zbMATH Keywords: uniqueness
zbMATH Keywords: fundamental solutions
zbMATH Keywords: p-Laplacian equation
zbMATH Keywords: asymptotic behaviour
zbMATH Keywords: porous medium equation
MaRDI profile type: Publication
OpenAlex ID: W2014270744
description: scientific article; zbMATH DE number 4146630