Analysis on the critical nonlinear wave equations in high dimensions and its applications

2014 Fiscal Year Final Research Report

• Project/Area Number: 24540183
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Future University-Hakodate
• Principal Investigator: TAKAMURA HIROYUKI 公立はこだて未来大学, システム情報科学部, 教授 (40241781)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: 非線形波動方程式 / 初期値問題 / 古典解 / 最大存在時間 / 時間大域存在 / 有限時間爆発

Outline of Final Research Achievements

The general theory for nonlinear wave equations is devoted to the estimate of the maximal existence time of classical solutions with small data. In high dimensions in which the spatial dimension is grater than 3, its optimality can be discussed only for the quadratic terms in four space dimensions. In such a case, the square of unknown functions itself is known to be a unique example of the nonlinear term which leads to the blow-up of the solution in finite time. The purpose of this study is to look for a criterion which classifies the nonlinear terms including the square of unknown functions into the global existence case or the blow-up case.

Free Research Field

非線形偏微分方程式