1. Existence of standing pulse solutions to a skew-gradient system
- Author
-
Jieun Lee and Y. S. Choi
- Subjects
Nonlinear system ,Applied Mathematics ,Gradient system ,Mathematical analysis ,Skew ,Pattern formation ,Type (model theory) ,Analysis ,Mathematics ,Sign (mathematics) ,Pulse (physics) - 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.
- Published
- 2021
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