Fundamental solutions and asymptotic behaviour for the p-Laplacian equation.

Soshana Kamin; Juan Luis Vázquez

Revista Matemática Iberoamericana (1988)

  • Volume: 4, Issue: 2, page 339-354
  • ISSN: 0213-2230

Abstract

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We establish the uniqueness of fundamental solutions to the p-Laplacian equationut = div (|Du|p-2 Du),   p > 2,defined for x ∈ RN, 0 < t < T. We derive from this result the asymptotic behavoir of nonnegative solutions with finite mass, i.e., such that u(*,t) ∈ L1(RN). Our methods also apply to the porous medium equationut = ∆(um),   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.

How to cite

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Kamin, Soshana, and Vázquez, Juan Luis. "Fundamental solutions and asymptotic behaviour for the p-Laplacian equation.." Revista Matemática Iberoamericana 4.2 (1988): 339-354. <http://eudml.org/doc/39371>.

@article{Kamin1988,
abstract = {We establish the uniqueness of fundamental solutions to the p-Laplacian equationut = div (|Du|p-2 Du),   p &gt; 2,defined for x ∈ RN, 0 &lt; t &lt; T. We derive from this result the asymptotic behavoir of nonnegative solutions with finite mass, i.e., such that u(*,t) ∈ L1(RN). Our methods also apply to the porous medium equationut = ∆(um),   m &gt; 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.},
author = {Kamin, Soshana, Vázquez, Juan Luis},
journal = {Revista Matemática Iberoamericana},
keywords = {Difusión; Ecuación de Laplace; Capa porosa; Gases; Soluciones; uniqueness; fundamental solutions; p-Laplacian equation; asymptotic behaviour; porous medium equation},
language = {eng},
number = {2},
pages = {339-354},
title = {Fundamental solutions and asymptotic behaviour for the p-Laplacian equation.},
url = {http://eudml.org/doc/39371},
volume = {4},
year = {1988},
}

TY - JOUR
AU - Kamin, Soshana
AU - Vázquez, Juan Luis
TI - Fundamental solutions and asymptotic behaviour for the p-Laplacian equation.
JO - Revista Matemática Iberoamericana
PY - 1988
VL - 4
IS - 2
SP - 339
EP - 354
AB - We establish the uniqueness of fundamental solutions to the p-Laplacian equationut = div (|Du|p-2 Du),   p &gt; 2,defined for x ∈ RN, 0 &lt; t &lt; T. We derive from this result the asymptotic behavoir of nonnegative solutions with finite mass, i.e., such that u(*,t) ∈ L1(RN). Our methods also apply to the porous medium equationut = ∆(um),   m &gt; 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.
LA - eng
KW - Difusión; Ecuación de Laplace; Capa porosa; Gases; Soluciones; uniqueness; fundamental solutions; p-Laplacian equation; asymptotic behaviour; porous medium equation
UR - http://eudml.org/doc/39371
ER -

Citations in EuDML Documents

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  1. Hua Shui Zhan, Large time behavior of solutions to a class of doubly nonlinear parabolic equations
  2. Abdelilah Gmira, Naji Yebari, Comportements asymptotiques des solutions d'équations paraboliques dégénénées sous des conditions optimales sur la donnée initiale
  3. Razvan Gabriel Iagar, Juan Luis Vázquez, Asymptotic analysis of the p -laplacian flow in an exterior domain
  4. Stephan Luckhaus, Yoshie Sugiyama, Large time behavior of solutions in super-critical cases to degenerate Keller-Segel systems

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