Displaying similar documents to “The dipole solution for the porous medium equation in several space dimensions”

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

Soshana Kamin, Juan Luis Vázquez (1988)

Revista Matemática Iberoamericana

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We establish the uniqueness of fundamental solutions to the p-Laplacian equation ut = 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 equation ut...

Initial traces of solutions to a one-phase Stefan problem in an infinite strip.

Daniele Andreucci, Marianne K. Korten (1993)

Revista Matemática Iberoamericana

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The main result of this paper is an integral estimate valid for non-negative solutions (with no reference to initial data) u ∈ L1 loc (Rn x (0,T)) to (0.1)   ut - Δ(u - 1)+ = 0,  in D'(Rn x (0,T)), for T > 0, n ≥ 1. Equation (0.1) is a formulation of a one-phase Stefan problem: in this connection...