Probabilistic representations of solutions to the heat equation View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2003-08

AUTHORS

B. Rajeev, S. Thangavelu

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. More... »

PAGES

321-332

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/bf02829609

DOI

http://dx.doi.org/10.1007/bf02829609

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1005568891


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