Generalized solutions of an inhomogeneous inviscid Burgers equation

Satyanarayana Engu (), M. Manasa () and P. B. Venkatramana ()
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Satyanarayana Engu: National Institute of Technology
M. Manasa: National Institute of Technology Karnataka
P. B. Venkatramana: National Institute of Technology Karnataka

Indian Journal of Pure and Applied Mathematics, 2022, vol. 53, issue 1, 188-206

Abstract: Abstract We derive generalized solutions of an inhomogeneous inviscid Burgers equation using vanishing viscosity method. This is achieved with the classical solution of a concerned viscous inhomogeneous Burgers equation. We then study Riemann problem for a de-coupled system. The weak solutions of the system are explicitly obtained by Volpert product concept. There are infinitely many real valued solutions for the system in the case of rarefaction wave and the weak solutions consist of $$\delta$$ δ - measures in the case of shock wave. Motivated by the structure of weak solutions, we construct the explicit generalized solutions for a more general de-coupled system.

Keywords: Vanishing viscosity; Weak solution; Volpert product; Reimann problem; 35Q53; 35B40; 35D30; 35D40 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s13226-021-00099-4

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