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Global existence and uniqueness of solutions for one-dimensional reaction-interface systems.
- Source :
-
Journal of Differential Equations . Jul2022, Vol. 324, p102-130. 29p. - Publication Year :
- 2022
-
Abstract
- In this paper, we provide a mathematical framework in studying the wave propagation with the annihilation phenomenon in excitable media. We deal with the existence and uniqueness of solutions to a one-dimensional free boundary problem (called a reaction–interface system) arising from the singular limit of a FitzHugh–Nagumo type reaction–diffusion system. Because of the presence of the annihilation, interfaces may intersect each other. We introduce the notion of weak solutions to study the continuation of solutions beyond the annihilation time. Under suitable conditions, we show that the free boundary problem is well-posed. [ABSTRACT FROM AUTHOR]
- Subjects :
- *THEORY of wave motion
Subjects
Details
- Language :
- English
- ISSN :
- 00220396
- Volume :
- 324
- Database :
- Academic Search Index
- Journal :
- Journal of Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- 156420215
- Full Text :
- https://doi.org/10.1016/j.jde.2022.04.004