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2017 Fiscal Year Final Research Report

Control of patterns by multicomponent reaction-diffusion systems of degenerate type

Research Project

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Project/Area Number 26610027
Research Category

Grant-in-Aid for Challenging Exploratory Research

Allocation TypeMulti-year Fund
Research Field Mathematical analysis
Research InstitutionTohoku University

Principal Investigator

Takagi Izumi  東北大学, 理学研究科, 名誉教授 (40154744)

Co-Investigator(Renkei-kenkyūsha) YAMAMOTO Hiroko  明治大学, 研究・知財戦略機構, 研究推進員 (10759153)
Research Collaborator LI Ying  Harbin Institute of Technology
Project Period (FY) 2014-04-01 – 2018-03-31
Keywords反応拡散方程式 / パターン形成 / 多成分 / 非拡散性成分 / 拡散性成分 / 不連続定常解
Outline of Final Research Achievements

A standard approach to modeling biological pattern formation has been based on the idea that the interaction between a slowly diffusing activator and a rapidly diffusing inhibitor results in spontaneous formation of spatial patterns. However, if the activator is a receptor attached on the cell membrane, it does not diffuse. Lately, reaction-diffusion models with non-diffusive activator and diffusive inhibitor have been proposed. In this project we studied rigorously the existence and stability of steady-state solutions of such model systems. We proved that there exist two types of steady states. Type I: the activator has jump discontinuity (but the inhibitor is continuous), and Type II: the activator is continuous. In addition, there exist continua of discontinuous steady states. Moreover, discontinuous steady states are stable, while continuous steady states are stable.

Free Research Field

非線型解析学

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Published: 2019-03-29  

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