GLOBAL EXISTENCE of SOLUTIONS of INITIAL-BOUNDARY VALUE PROBLEM with NONLINEAR NONLOCAL BOUNDARY CONDITION for NONLINEAR NONLOCAL PARABOLIC EQUATION with ABSORPTION

Classical solutions of the initial-boundary value problem with a nonlinear nonlocal boundary condition for a nonlinear nonlocal parabolic equation with absorption are considered. The comparison principle of solutions of this problem is proved. No additional assumptions are made for the case when nonlinearities in absorption do not satisfy the Lipschitz condition. Conditions are found under which the solutions exist globally or becomes infinite in a finite time. The results obtained improve those established earlier by other authors