Iterative approximation of solutions for semilinear parabolic equations system

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 R n × R + and subject to Cauchy boundary conditions on R n , 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.