Nonlinear parabolic equations in sections of vector bundles
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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