DYNAMICS OF NONLINEAR ANOMALOUS REACTION-DIFFUSION MODELS: GLOBAL EXISTENCE AND BLOW-UP OF SOLUTIONS

Jabbarkhanov K. Suragan D.
October 2025 American Institute of Mathematical Sciences

Evolution Equations and Control Theory
2025 #14 Issue 5 1128 - 1140 pp.

In this paper, we investigate a large class of nonlinear reaction-diffusion models with fractional Laplacians. We employ a combination of the concavity method and the first-order differential inequality technique to establish the necessary conditions for both global existence and blow-up solutions. We also illustrate our main results through concrete examples.

blow-up solution , concavity method , first-order differential inequality technique , fractional p-sub-Laplacian , fractional Poincaré inequality , Fractional reaction-diffusion model , global solution

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Department of Mathematics, Nazarbayev University, Astana, 010000, Kazakhstan
Institute of Mathematics and Mathematical Modeling, Almaty, 050010, Kazakhstan
International School of Economics, Maqsut Narikbayev University, Astana, 010000, Kazakhstan

Department of Mathematics
Institute of Mathematics and Mathematical Modeling
International School of Economics

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