Study on the existence and uniqueness of solutions for systems of conservation laws

Research Project

Project/Area Number	25800075
Research Category	Grant-in-Aid for Young Scientists (B)
Allocation Type	Multi-year Fund
Research Field	Mathematical analysis
Research Institution	Niigata University
Principal Investigator	OHWA HIROKI 新潟大学, 自然科学系, 助教 (10549158)
Project Period (FY)	2013-04-01 – 2015-03-31
Project Status	Completed (Fiscal Year 2014)
Budget Amount *help	¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000) Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000) Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywords	実解析 / 保存則方程式 / 非線形現象
Outline of Final Research Achievements	A proof of global existence of solutions with small total variation, to the Cauchy problem for one-dimensional n×n systems of conservation laws is appeared in the papers of A. Bressan (1992) and N. H. Risebro (1993). The proof relies on the wave-front tracking method. The wave-front tracking method is one of the famous methods of the proof. We give a simple argument in the wave-front tracking method and clearly prove the global existence of solutions for those systems. Moreover, as preparations to study the uniqueness of the solutions, we classify the discontinuities and obtain periodic properties of some piecewise linear functions.