Probabilistic representations of solutions to the heat equation

B. Rajeev; S. Thangavelu

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Probabilistic representations of solutions to the heat equation

B. Rajeev·S. Thangavelu

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Abstract

In this paper we provide a new (probabilistic) proof of a classical result in partial differential equations, viz. if $ϕ$ is a tempered distribution, then the solution of the heat equation for the Laplacian, with initial condition $ϕ$, is given by the convolution of $ϕ$ with the heat kernel (Gaussian density). Our results also extend the probabilistic representation of solutions of the heat equation to initial conditions that are arbitrary tempered distributions.

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BibTeX RIS

B. Rajeev, S. Thangavelu. 2003-10-17. Probabilistic representations of solutions to the heat equation. https://arxiv.org/abs/math/0310262

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