A Riemann problem whose viscosity solutions contain \(\delta\)-measures. (English) Zbl 0791.35077
Summary: The author studies the Riemann problem for a \(2\times 2\) system of conservation laws, whose solution need not be real-valued functions, but may contain \(\delta\)-measures concentrated along some curves. He considers a parabolic approximation of the Riemann problem and obtains an explicit formula. Then the solution of the Riemann problem is obtained as the limit of this approximate solution.
MSC:
35L60 | First-order nonlinear hyperbolic equations |
35D05 | Existence of generalized solutions of PDE (MSC2000) |
49L25 | Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games |
35L65 | Hyperbolic conservation laws |
35Q53 | KdV equations (Korteweg-de Vries equations) |
35A20 | Analyticity in context of PDEs |