Cauchy problem of hyperbolic conservation laws in multidimensional space with intersecting jump initial data

Abstract:

Cauchy problem of hyperbolic conservation laws in multidimensional space is considered, where the initial data have several jump discontinuity surfaces which develop into shock fronts intersecting at a common submanifold. Local existence is proved, assuming compatible conditions and uniform stability. For isentropic flow in $2$-dimensional space, the interaction of two shock fronts and the nonexistence of three intersecting shock fronts are discussed.