Iterative approximation of solutions for semilinear parabolic equations system

摘要

In this paper we present the convergence analysis of iterative schemes for solving semilinear systems resulting from multidimensional semilinear second-order parabolic partial differential equations (PDEs) defined in a domain Rn×R+ and subject to Cauchy boundary conditions on Rn, using the method of integral successive iterative approximation and the principle of decay estimation, we derive the bounded, nonnegative, local solutions and global solutions. Blowing-up results of the solutions are also presented.