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DOI: 10.23952/jnfa.2024.29
Received May 3, 2024; Accepted September 6, 2024; Published December 9, 2024
Abstract. 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.
How to Cite this Article:
I.M. Batiha, O. Ogilat, Z. Chebana, T.E. Oussaeif, N. Anakira, A. Amourah, S. Momani, Finite-time blow-up and solvability for a semilinear parabolic problem with nonlinear integral conditions, J. Nonlinear Funct. Anal. 2024 (2024) 29.