关键词: Nonlinear parabolic systems with measurable coefficients, initial-oblique derivative problems, multiply connected domains

Abstract:

This paper deals with some initial-oblique derivative boundary value problems for nonlinear nondivergent parabolic systems of several second order equations with mea-surable coefficients in multiply connected domains. Firstly, a priori estimates of solutions for the initial-boundary value problems are given, and then by using the above estimates of solutions and the Leray-Schauder theorem, the existence and uniqueness of solutions for
the problems are proved.

Key words: Nonlinear parabolic systems with measurable coefficients, initial-oblique derivative problems, multiply connected domains