A Riemann problem whose viscosity solutions contain δ-measures

Article type: Research Article

Authors: Joseph, K.T.^;

Affiliations: T.I.F.R. Centre, P.B. No. 1234, 1.1.Sc. Campus, Bangalore 560 012, India

Note: [] Correspondence to: K.T. Joseph, T.I.F.R. Centre, P.B. No. 1234, I.I.Sc. Campus, Bangalore 560 012, India.

Note: [] Dedicated to the memory of Professor K.G. Ramanathan

Abstract: In this paper we study the Riemann problem for a 2×2 system of conservation laws, whose solution need not be real-valued functions, but may contain δ-measures concentrated along some curves. We consider a parabolic approximation of the Riemann problem and obtain an explicit formula. Then the solution of the Riemann problem is obtained as the limit of this approximate solution.

DOI: 10.3233/ASY-1993-7203

Journal: Asymptotic Analysis, vol. 7, no. 2, pp. 105-120, 1993