Finite-time blow-up and solvability for a semilinear parabolic problem with nonlinear integral conditions
Journal of Nonlinear Functional Analysis · 2024
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.