Journal
JOURNAL OF DIFFERENTIAL EQUATIONS
Volume 337, Issue -, Pages 460-482Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2022.08.007
Keywords
Reaction-diffusion equations; Stationary solutions; Stability; Close-to-equilibrium patterns
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This study investigates a general system consisting of several ordinary differential equations and a reaction-diffusion equation in a bounded domain. The main finding is the instability of all regular patterns, suggesting that stable stationary solutions in models with non-diffusive components must be far-from-equilibrium and exhibit singularities.
A general system of several ordinary differential equations coupled with a reaction-diffusion equation in a bounded domain with zero-flux boundary condition is studied in the context of pattern formation. These initial-boundary value problems may have regular (i.e. sufficiently smooth) stationary solutions. This class of close-to-equilibrium patterns includes stationary solutions that emerge due to the Turing instability of a spatially constant stationary solution. The main result of this work is instability of all regular patterns. It suggests that stable stationary solutions arising in models with non-diffusive components must be far-from -equilibrium exhibiting singularities. Such discontinuous stationary solutions have been considered in our parallel work (Cygan et al., 2021 [4]). (c) 2022 Elsevier Inc. All rights reserved.
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