Generalized Solutions of Nonlinear Parabolic Equations and Diffusion Processes

• Autores: Ya. Belopolskaya, W. A. Woyczynski
• Localización: Acta applicandae mathematicae, ISSN 0167-8019, Vol. 96, Nº. 1-3, 2007, págs. 55-69
• Idioma: inglés
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• Resumen

  • 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.