| Abstract: | 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.
Translated fromProblemy Matematicheskogo Analiza, No. 13, 1992, pp. 19–42. |
