Global Existence of solutions for systems of coupled reaction diffusion equations with nonlinearities of unlimited growth

2023/01/18 by Saïd Kouachi, Kouachi, Said
Engineering · Mathematics · Medicine · #35K57 #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models #Primary 35K45 #Secondary 35K45 #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2301.07708

openalex publication_date 2023/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work we prove global existence and uniform boundedness of solutions of 2X2 reaction-diffusion systems with control of mass structure and nonlinearities of unlimited growth. Furthermore the results are obtained without restrictions on diffusion terms neither on the initial data. Such systems possess many applications in physical-chemistry. Our technique of proof relies on a judiciously rectified Lyapunov functional used previously by the author in several papers

Related

• Global existence for reaction diffusion systems with strict balance Law and nonlinearities with non constant-sign and unlimited polynomial growth
• Global existence in reaction-diffusion systems with mass control under relaxed assumptions merely referring to cross-absorptive effects
• Global Existence of Solutions to Reaction Diffusion Systems with Mass\n Transport Type Boundary Conditions on an Evolving Domain
• Global existence for coupled reaction-diffusion equations with a balance law and nonlinearities with non-constant sign
• Global existence for reaction-diffusion systems on multiple domains