Spike solutions for a mass conservation reaction-diffusion system

Shin-Ichiro Ei; Shyuh-Yaur Tzeng

doi:10.3934/dcds.2020049

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2020, Volume 40, Issue 6: 3357-3374. Doi: 10.3934/dcds.2020049 open access

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Next Article Free boundary problem for a reaction-diffusion equation with positive bistable nonlinearity

Spike solutions for a mass conservation reaction-diffusion system

Shin-Ichiro Ei^1, , and
Shyuh-Yaur Tzeng^2,

1.
Department of Mathematics, Faculty of Science, Hokkaido University, Sapporo 060-0810, Japan
2.
Department of Mathematics, National Changhua University of Education, Changhua, Taiwan

^* Corresponding author: Shin-Ichiro Ei
^* Corresponding author: Shin-Ichiro Ei

Received: February 28, 2019

Revised: June 30, 2019

Published: March 2020

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Abstract

This article deals with a mass conservation reaction-diffusion system. As a model for studying cell polarity, we are interested in the existence of spike solutions and some properties related to its dynamics. Variational arguments will be employed to investigate the existence questions. The profile of a spike solution looks like a standing pulse. In addition, the motion of such spikes in heterogeneous media will be derived.

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Mathematics Subject Classification: Primary: 35B25, 35J505, 35K57; Secondary: 37L6.

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