engleski

Singular solutions of a fully nonlinear 2x2 system of conservation laws

We prove existence of singular solution to the Brio system. It is the system of conservation laws which is nonlinear with respect to both unknowns. The system is fully nonlinear, i.e. it is nonlinear with respect to both unknowns, and it does not admit the classical Lax-admissible solution for certain Riemann problems. By introducing complex-valued corrections in the framework of the weak asymptotic method, we show that a compressive δ-shock solution resolves such Riemann problems. By letting the approximation parameter tend to zero, the corrections become real valued, and the solutions can be seen to fit into the framework of weak singular solutions defined by Danilov and Shelkovich. Indeed, in this context, we can show that every 2 × 2 system of conservation laws admits δ-shock solutions.

Brio system; conservation laws; singular solutions

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