Pinned fronts in heterogeneous media of jump type

Peter Van Heijster; Arjen Doelman; Tasso J. Kaper; Yasumasa Nishiura; Kei Ichi Ueda

doi:10.1088/0951-7715/24/1/007

Pinned fronts in heterogeneous media of jump type

Peter Van Heijster, Arjen Doelman, Tasso J. Kaper, Yasumasa Nishiura, Kei Ichi Ueda

Advanced Institute for Materials Research (AIMR)

Research output: Contribution to journal › Article › peer-review

20 Citations (Scopus)

Abstract

In this paper, we analyse the impact of a (small) heterogeneity of jump type on the most simple localized solutions of a 3-component FitzHugh-Nagumo- type system. We show that the heterogeneity can pin a 1-front solution, which travels with constant (non-zero) speed in the homogeneous setting, to a fixed, explicitly determined, distance from the heterogeneity. Moreover, we establish the stability of this heterogeneous pinned 1-front solution. In addition, we analyse the pinning of 1-pulse, or 2-front, solutions. The paper is concluded with simulations in which we consider the dynamics and interactions of N-front patterns in domains with M heterogeneities of jump type (N = 3, 4, M ≥ 1).

Original language	English
Pages (from-to)	127-157
Number of pages	31
Journal	Nonlinearity
Volume	24
Issue number	1
DOIs	https://doi.org/10.1088/0951-7715/24/1/007
Publication status	Published - 2011 Jan

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
Physics and Astronomy(all)
Applied Mathematics

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AU - Van Heijster, Peter

AU - Doelman, Arjen

AU - Kaper, Tasso J.

AU - Nishiura, Yasumasa

AU - Ueda, Kei Ichi

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Pinned fronts in heterogeneous media of jump type

Abstract

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