On Regularity of All Weak Solutions and Their Attractors for Reaction-Diffusion Inclusion in Unbounded Domain

Скiнченновимiрнiсть динамiки з точнiстю до малого параметра включення типу реакцiї-дифузiї в необмеженiй областi

“…The following three lemmas from [5] will be used in the proof of Theorem 2.1. and for all t ≥ T (ε, B) and k ≥ K(ε, B) the next inequality holds:…”

“…There are a lot of papers on qualitative behavior of solutions for evolution systems of reactiondiffusion type. It caused by the theoretical and applied significance of such objects [5,8,13,16,20]. The particular cases of reaction-diffusion problems are Kolmogorov -Petrovskiy -Piskunov equations (the problem on the gene diffusion) [9], models of Belousov -Zhabotinsky reaction [3,15], Gause -Vitta models [17,18], Selkov model for glycolysis [10,14] etc.…”

Lyapunov Functions for Differential Inclusions and Applications in Physics, Biology, and Climatology

“…Topological properties of strong and weak solutions were considered in [14,[31][32][33][34]. Regularity properties of global and trajectory attractors were provided in [18,[24][25][26] (14.5), is a Lyapunov type function for K + . Moreover, for each u ∈ K + and all τ and T , 0 < τ < T < ∞, the energy equality holds…”

Regularity of global attractors for reaction-diffusion systems with no more than quadratic growth

“…The question about the regularity of solutions for reaction-diffusion equations and inclusions without uniqueness is an important and interesting task, which has been studied recently in several works (see e.g. [2], [5], [7], [18]).…”