Ill-posedness of the Cauchy problem for totally degenerate system of conservation laws

Electronic Journal of Differential Equations

关键词: Conservation laws;    Cauchy problem;    totally degenerated systems;    ill-posed.;   

DOI  :  

来源: DOAJ

【 摘 要 】

In this paper we answer some open questions concerning totallydegenerate systems of conservation laws. We study the augmentedBorn-Infeld system, which is the Born-Infeld model augmented bytwo additional conservations laws. This system is a nice exampleof totally degenerate system of conservation laws and, globalsmooth solutions are conjectured to exist when the initial-data issmooth. We show that this conjecture is false, for the morenatural and general condition of initial-data. In fact, first weshow that does not exist global smooth solution for any 2X2totally degenerated system of conservation laws, which thecharacteristics speeds do not have singular points. Moreover, wesharpen the conjecture in Majda [20]. Under the samehypothesis of initial-data, we show that the Riemann Problem isnot well-posed, which follows for weak solutions of the CauchyProblem. In the end, we prove some results on the direction ofwell-posedness for the less physically initial-data.

【 授权许可】

Unknown