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

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 -