GLOBAL BEHAVIOR OF SOLUTIONS TO THE NONLOCAL IN TIME REACTION-DIFFUSION EQUATIONS
Torebek B.T.
August 2025American Institute of Mathematical Sciences
Evolution Equations and Control Theory
2025#14Issue 4733 - 747 pp.
This paper addresses the Cauchy-Dirichlet problem in the context of time-nonlocal reaction-diffusion equations, specifically focusing on the equation (Formula Presented) where (Formula Presented), f is a locally Lipschitz function, and Lx is a linear operator. This model is particularly relevant for studying anomalous and ultraslow diffusion processes. Our research contributes to the understanding of this equation by presenting results on local and global existence, decay estimates, and conditions leading to the blow-up of solutions. These findings provide answers to some of the questions raised earlier by Gal and Warma in [C. G. Gal, M. Warma, Springer Nature, Switzerland AG., 2020.] and also by Luchko and Yamamoto in [Y. Luchko, M. Yamamoto, Fract. Calc. Appl. Anal., 19:3 (2016), 676–695]. Additionally, the paper explores potential quasi-linear extensions of these results and outlines several open questions for future research.
decay estimate , global existence , reaction-diffusion equation , Sonine kernel
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Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Belgium
Institute of Mathematics and Mathematical Modeling
Department of Mathematics: Analysis
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026