Study of evolution equations in the space of BV functions

2014 Fiscal Year Final Research Report

• Project/Area Number: 23540239
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Global analysis
• Research Institution: Shizuoka University
• Principal Investigator: KIKUCHI Koji 静岡大学, 工学研究科, 教授 (50195202)
• Co-Investigator(Kenkyū-buntansha): SHIMIZU Senjo 静岡大学, 理学研究科, 教授 (50273165) ; HOSHIGA Akira 静岡大学, 工学研究科, 准教授 (50261400) ; ADACHI Shinji 静岡大学, 工学研究科, 准教授 (40339685) ; NAKAJIMA Toru 静岡大学, 工学研究科, 准教授 (50362182)
• Project Period (FY): 2011-04-28 – 2015-03-31
• Keywords: 函数方程式論 / 函数解析学

Outline of Final Research Achievements

In this research we obtained that for a quasilinear hyperbolic equation, if the initial data is sufficiently small, then a solution behaves like a solution to the linearlized equation, and that for the equation of motion of vibrating membrane with a kind of strong viscosity term, if the initial data is slightly regular (but twice differentability is suficient) , there is a unique solution in the space of BV functions. But this strong viscosity term does not have variational structure. We hope to obtain the same results for the equation of motion of vibrating membrane with a strong viscosity term which has variational structure. In the period of our research we only develope our analysis in Sobolev spaces, and it is not extended to the theory in the space of BV functions.

Free Research Field

偏微分方程式