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arXiv · 1910.13544

Existence of standing pulse solutions to a skew-gradient system

Yung-Sze Choi·Jieun Lee
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Abstract

Reaction-diffusion systems have been primary tools for studying pattern formation. A skew-gradient system is well known to encompass a class of activator-inhibitor type reaction-diffusion systems that exhibit localized patterns such as fronts and pulses. While there is a substantial literature for the case of a linear inhibitor equation, the study of nonlinear inhibitor effect is still limited. To fill this research gap, we investigate standing pulse solutions to a skew-gradient system in which both activator and inhibitor reaction terms inherit nonlinear structures. Using a variational approach that involves several nonlocal terms, we establish the existence of standing pulse solutions with a sign change. In addition, we explore some qualitative properties of the standing pulse solutions.

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Yung-Sze Choi, Jieun Lee. 2019-10-29. Existence of standing pulse solutions to a skew-gradient system. https://arxiv.org/abs/1910.13544

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