This paper studies the dynamics of the generalized Lengyel-Epstein reaction-diffusion model proposed in a recent study by Abdelmalek and Bendoukha.Two main results are shown in this paper. The first of which is sufficient conditions that guarantee the nonexistence of Turing patterns, ie, nonconstant solutions.Second, more relaxed conditions are derived for the stability of the system's unique steady-state solution.
KEYWORDSgeneralized Lengyel-Epstein model, global asymptotic stability, Lyapunov functional Math Meth Appl Sci. 2017;40:6295-6305.wileyonlinelibrary.com/journal/mma
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.
Local and blowing‐up solutions for the Cauchy problem for a system of space and time fractional evolution equations with time‐nonlocal nonlinearities of exponential growth are considered. The existence and uniqueness of the local mild solution is assured by the Banach fixed point principle. Then, we establish a blow‐up result by Pokhozhaev capacity method. Finally, under some suitable conditions, an estimate of the life span of blowing‐up solutions is established.
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