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Riemann problem for rate-type materials with non-constant initial conditions
  • R. Radha,
  • Vishnu Dutt Sharma,
  • Akshay Kumar
R. Radha
Univ Hyderabad

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Vishnu Dutt Sharma
Indian Institute of Technology Gandhinagar
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Akshay Kumar
University of Hyderabad
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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 characterisation of the solutions.
21 Feb 2021Submitted to Mathematical Methods in the Applied Sciences
23 Feb 2021Assigned to Editor
23 Feb 2021Submission Checks Completed
13 Mar 2021Reviewer(s) Assigned
02 Jun 2021Review(s) Completed, Editorial Evaluation Pending
05 Jun 2021Editorial Decision: Accept