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Generalized Solutions of Nonlinear Parabolic Equations and Diffusion Processes |
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| Authors: | Ya. Belopolskaya W. A. Woyczynski |
| Affiliation: | (1) Department of Mathematics, St. Petersburg State University for Architecture and Civil Engineering, St. Petersburg, Russia;(2) Department of Statistics, and Center for Stochastic and Chaotic Process in Science and Technology, Case Western Reserve University, Cleveland, OH 44106, USA |
| Abstract: | We reduce the construction of a weak solution of the Cauchy problem for a quasilinear parabolic equation to the construction of a solution to a stochastic problem. Namely, we construct a diffusion process that allows us to obtain a probabilistic representation of a weak (in distributional sense) solution to the Cauchy problem for a nonlinear PDE. |
| Keywords: | Stochastic flows Diffusion process Nonlinear parabolic equations Cauchy problem |
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