FINITE-TIME BLOW-UP AND SOLVABILITY FOR A SEMILINEAR PARABOLIC PROBLEM WITH NONLINEAR INTEGRAL CONDITIONS

This paper is devoted to the study of a super-linear non-local problem with Neumann condition modeling by the integral condition of second type for a class of reaction-diffusion equations. We show the existence of the weak solution by developing the method of Fadeo-Galarkin to avoid the complexities produced by the existence of the integral condition. Then, by applying an a priori estimate, we prove the uniqueness of the weak solution to the problem. We also study the finite-time blow-up solution.