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

Jean-François Le Gall

International Journal of Stochastic Analysis, 1996, vol. 9, 1-16

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.

Date: 1996
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijsa:953087

DOI: 10.1155/S1048953396000354

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