Ray equations of a weak shock in a hyperbolic system of conservation laws in multi-dimensions

Proceedings Mathematical Sciences

Phoolan Prasad¹ 

[1] Department of Mathematics, Indian Institute of Science, Bangalore 0 0, India$$

关键词: Ray theory;    nonlinear waves;    conservation laws;    shock propagation and weak curved shock.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

In this paper we give a complete proof of a theorem, which states that ‘for a weak shock, the shock ray velocity is equal to the mean of the ray velocities of nonlinear wavefronts just ahead and just behind the shock, provided we take the wavefronts ahead and behind to be instantaneously coincident with the shock front. Similarly, the rate of turning of the shock front is also equal to the mean of the rates of turning of such wavefronts just ahead and just behind the shock’. A particular case of this theorem for shock propagation in gasdynamics has been used extensively in applications. Since it is useful also in other physical systems, we present here the theorem in its most general form.

【 授权许可】

Unknown