Nonlinear parabolic equations in sections of vector bundles
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We study the Cauchy problem for a nonlinear parabolic equation relative to a section of a vector bundle. The special procedure of covariant differential extension makes it possible to reduce this equation to a system of quasilinear parabolic equations, which can be studied using the theory of stochastic equations. We obtain a probabilistic representation of the solution of both the auxiliary quasilinear parabolic system and the original nonlinear equation. Bibliography: 5 titles.
KeywordsCauchy Problem Probabilistic Representation Vector Bundle Nonlinear Equation Parabolic Equation
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- 2.Ya. I. Belopol'skaya and Yu. L. Daletskii, “A study of the Cauchy problem for quasilinear parabolic equations and systems with finite and infinite numbers of arguments using Markov stochastic processes,”Izv. Vuzov, Ser. Mat., No. 6, 5–17 (1978).Google Scholar
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