Global classical solutions for reaction–diffusion systems with nonlinearities of exponential growth

Abstract

Abstract. The aim of this study is to prove global existence of classical solutions for problems of the form solutions as t goes to +∞ is also studied. For this purpose, we use the appropriate techniques which are based on semigroups, energy estimates and Lyapunov functional methods.

Global existence for a strongly coupled reaction-diffusion systems with nonlinearities of exponential growth

“…The present investigation is a continuation of results obtained in [24]. In this study, we will treat the case of a general full matrix of diffusion coefficients and prove that if f and g satisfying (A1)-(A4), then Σ is an invariant region for problem (1.1)-(1.4).…”

“…problem (1.1)-(1.4) is equivalent to a problem for which the global existence follows from the technique based on Lyapunov functional method (see, e.g., [3], [8], [14], [16], [18], [21] and [24]).…”

“…Our goal is to understand how the results of the diagonal case extend to the nondiagonal situation without any additional assumption on the diffusion coefficients in the case of possiblity of growth faster than exponential for the reaction terms. For this purpose, we construct the invariant regions in which we can demonstrate that for any initial data in this regions satisfying (1.6), problem (1.1)-(1.4) is equivalent to a problem for which the global existence follows from the same Lyapunov functional used in [24] when the reactive terms satisfies (A1)-(A4).…”

A uniform bound for solutions to a thermo-diffusive system

“…All of these papers considered the problem on a bounded domain Ω ⊂ R n . For a particular class of super-exponential nonlinearity, global existence and uniform bound of solution for L ∞ small initial data in a bounded domain have been proved in [39].…”

Generalized Result on Global Existence of Weak Solutions for Parabolic Reaction-Diffusion Systems

“…Rebiai and Benachour [28] have treated the case of a general full matrix of diffusion coefficients with homogeneous boundary conditions and non-linearities of exponential growth.…”