Generalized Solutions of Nonlinear Parabolic Equations and Diffusion Processes
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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.
KeywordsStochastic flows Diffusion process Nonlinear parabolic equations Cauchy problem
Mathematics Subject Classification (2000)60H10 60J60 35G05 35K45
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