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Riemann problem for rate-type materials with nonconstant initial conditions
Mathematical Methods in the Applied Sciences ( IF 2.9 ) Pub Date : 2021-07-29 , DOI: 10.1002/mma.7663
R. Radha 1 , Vishnu Dutt Sharma 2 , Akshay Kumar 1
Affiliation  

In this paper, using the compatible theory of differential invariants, a class of exact solutions is obtained for nonhomogeneous quasilinear hyperbolic system of partial differential equations (PDEs) describing rate type materials; these solutions exhibit genuine nonlinearity that leads to the formation of discontinuities such as shocks and rarefaction waves. For certain nonconstant and smooth initial data, the solution to the Riemann problem is presented providing a complete characterization of the solutions.

中文翻译:

具有非恒定初始条件的速率型材料的黎曼问题

本文利用微分不变量的相容理论,得到了描述速率型材料的偏微分方程(PDEs)的非齐次拟线性双曲系统的一类精确解;这些解决方案表现出真正的非线性,导致形成不连续性,如冲击和稀疏波。对于某些非常量和平滑的初始数据,提供了黎曼问题的解决方案,提供了解决方案的完整表征。
更新日期:2021-07-29
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