A probabilistic approach to the trace at the boundary for solutions of a semilinear parabolic partial differential equation. (1996)

• Record Type: Journal Article
• Authors: Gall, Jean-François Le
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 9:Number 4(1996)
• Page Start: 399
• Page End: 414
• Publication Date: 1996
• Subjects: parabolic partial differential equation -- boundary trace -- Brownian snake -- probabilistic representation -- additive functionals -- polar sets -- maximal solutions; Mathematical models -- Periodicals; Computer simulation -- Periodicals; Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Computer simulation; Mathematical models; Applied Mathematics; Periodicals; Electronic journals; 519.22
• DOI: 10.1155/S1048953396000354
• Languages: English
• ISSNs: 1048-9533

Abstract

Abstract : We use the path-valued process called the “Brownian snake” to investigate the trace at the boundary of nonnegative solutions of a semilinear parabolic partial differential equation. In particular, we characterize possible traces and in dimension one we prove that nonnegative solutions are in one-to-one correspondence with their traces at the origin. We also provide probabilistic representations for various classes of solutions. This article is dedicated to the memory of Roland L. Dobrushin.