Analysis of interfacial phenomena and singularities in nonlinear partial differential equations

2015 Fiscal Year Final Research Report

• Project/Area Number: 25800071
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Mathematical analysis
• Research Institution: Iwate University
• Principal Investigator: Nara Mitsunori 岩手大学, 人文社会科学部, 准教授 (90512161)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: 偏微分方程式 / 反応拡散方程式 / 界面現象 / 進行波

Outline of Final Research Achievements

This research mainly deals with the following topics; (1) singular limit problem of damped wave equations with bistable-type nonlinearity on the multi-dimensional whole space, where some estimates for generation and motion of interfaces are obtained, (2) stability of one-dimensional traveling wave solutions in the damped wave equations with bistable-type nonlinearity is analyzed, and some sufficient conditions for such the stability is shown, (3) asymptotic behavior of solutions with spreading fronts in the Cauchy problem of anisotropic Allen-Cahn equations is studied, where it is revealed that the notions of Frank diagram and Wulff shape play important roles.

Free Research Field

非線形解析