Finite-time blow-up and solvability of a weak solution for a superlinear reaction-diffusion problem with integral conditions of the second type
Abstract
The focus of this work is on a class of reaction-diffusion equations: a superlinear nonlocal issue with Neumann condition modeled by the integral condition of second type. By using the Fadeo-Galarkin method to get over the complications caused by the integral condition’s existence, we are able to demonstrate the existence of the weak solution. Next, we demonstrate the uniqueness of the problem’s weak solution by using an a priori estimate. In conclusion, we examine the blow-up solution for completeness in its finite-time case.
Copyright © 2024 Iqbal M. Batiha, Iqbal H. Jebril, Zainouba Chebana, Taki-Eddine Oussaeif, Sofiane Dehilis, Shawkat Alkhazaleh. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
I. M. Batiha, I. H. Jebril, Z. Chebana, T.-E. Oussaeif, S. Dehilis, S. Alkhazaleh, Finite-time blow-up and solvability of a weak solution for a superlinear reaction-diffusion problem with integral conditions of the second type, Adv. Fixed Point Theory 14 (2024), 45. https://doi.org/10.28919/afpt/8708
BibTeX
@article{Batiha2024,
author = {Batiha, Iqbal M. and Jebril, Iqbal H. and Chebana, Zainouba and Oussaeif, Taki-Eddine and Dehilis, Sofiane and Alkhazaleh, Shawkat},
title = {Finite-time blow-up and solvability of a weak solution for a superlinear reaction-diffusion problem with integral conditions of the second type},
journal = {Adv. Fixed Point Theory},
volume = {14},
year = {2024},
pages = {45},
doi = {10.28919/afpt/8708}
}