A weak asymptotic solution developed by Panov and Shelkovich, is constructed for piecewise known solutions to a prolonged system of conservation laws by introducing δ, δ' , δ'' and δ''' waves along a discontinuity curve, which in turn implies the existence of weak asymptotic solutions for the Riemann type initial data. By piecing together the Riemann problems, weak asymptotic solution is constructed for general type of initial data. Further entropy weak asymptotic solution for a prolonged system of conservation laws and as a special case for Riemann type initial data is constructed.
School of Mathematical Sciences
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