SOLUTION COMPARISON PRINCIPLE OF THE INITIAL-BOUNDARY VALUE PROBLEM FOR A SYSTEM OF SEMILINEAR PARABOLIC EQUATIONS WITH NONLINEAR NONLOCAL BOUNDARY CONDITIONS
We consider the initial-boundary value problem for a system of semilinear parabolic equations with nonlinear nonlocal boundary conditions. The aim of this work is to prove the comparison principle of solutions of initial-boundary value problem. In this paper we use the methods of the theory of partial differential equations. The comparison principle for solutions of initial-boundary value problem for a system of semilinear parabolic equations with nonlinear nonlocal boundary conditions and nonnegative initial data is proved. The finding can be used to study partial differential equations.