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An asymptotic expansion for the solution of the generalized Riemann problem. I: General theory. (English) Zbl 0679.35064
The following generalized Riemann problem for nonlinear hyperbolic systems of conservation laws is considered: \[ u_ t+f(x,t,u)_ x=g(x,t,u),\quad x\in R,\quad t>0,\quad u\in R^ p, \] u(x,0) is smooth for \(x<0\) and \(x>0\). An entropy solution of this problem is found in the form of an asymptotic expansion in time of the type \[ v(z,t)=u(zt,t),\quad v(z,t)=v_ 0(z)+tv_ 1(z)+...+t^ kv_ k(z)+.... \] An explicit method of construction of this asymptotic expansion is given and an approximate solution is constructed in a suitable way from the truncated expansion. \(L^ 1\)-bound for the error of such an approximation is given.
Reviewer: A.Doktor

35L65 Hyperbolic conservation laws
35A35 Theoretical approximation in context of PDEs
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