STRUCTURE OF ENTROPY SOLUTIONS TO SCALAR CONSERVATION LAWS WITH STRICTLY CONVEX FLUX

被引：17

作者：

Adimurthi ^{[1
]}

Ghoshal, Shyam Sundar ^{[1
]}

Gowda, G. D. Veerappa ^{[1
]}

机构：

[1] Tata Inst Fundamental Res, Ctr Applicable Math, Bangalore 560065, Karnataka, India

来源：

JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS | 2012年 / 9卷 / 04期

关键词：

Hamilton-Jacobi equation; scalar conservation laws; characteristic lines; asymptotically single shock packet; ASYMPTOTIC-BEHAVIOR;

D O I：

10.1142/S0219891612500191

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider scalar conservation laws in one space dimension with convex flux and we establish a new structure theorem for entropy solutions by identifying certain shock regions of interest, each of them representing a single shock wave at infinity. Using this theorem, we construct a smooth initial data with compact support for which the solution exhibits infinitely many shock waves asymptotically in time. Our proof relies on Lax-Oleinik explicit formula and the notion of generalized characteristics introduced by Dafermos.

引用

页码：571 / 611

页数：41

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