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Envelope method and new structure of solutions of multi-dimensional scalar conservation law equations and related problems

组织者

丘成栋

演讲者

杨小舟

时间

2022年09月23日 16:00 至 16:30

地点

Online

线上

Tencent 639 1488 3821 ()

摘要

In this talk, we will discuss some new singular structures of shock waves, rarefaction waves and their interactions in the multi-dimensional scalar conservation law, as well as some relevant results, the talk contains following parts: (1) We present the necessary and sufficient conditions for the generation of plus and minus envelopes of non-selfsimilar rarefaction waves in the case of two-dimensional conservation laws, meanwhile, all kinds of solution structures are classified, and some new global singular properties of interactions between shock waves and rarefaction waves are be obtained and proved under the envelope method and the above necessary and sufficient conditions, we also prove the uniqueness of these new structures. (2) In the case of general n-dimensional homogeneous and non-homogeneous scalar conservation law, the global structures of non-selfsimilar shock wave solutions and rarefaction wave solutions are obtained, especially when the non-homogeneous term does not satisfy the Lipschitz condition, we find particular phenomena of basic wave solutions. Above results are joint works with Gaowei Cao, Hui Kan, Guiqin Qiu, Wei Xiang and Yuanan Zhao.