Entropy solution

Summary

An entropy solution of a scalar conservation law $u_t + \operatorname{div} f(u) = 0$ is a weak solution that also satisfies a family of inequalities, the entropy conditions. Weak solutions of conservation laws are in general not unique, because shocks can be drawn in many ways. The entropy conditions select the physically relevant solution, the one obtained as the limit of solutions with small added viscosity. In Kruzhkov's formulation, the entropy solution of the initial value problem exists and is unique for every bounded initial datum.