PIECEWISE SMOOTH SOLUTIONS OF SEMILINEAR HYPERBOLIC SYSTEMS IN HIGHER SPACE DIMENSION

This paper discusses piecewise smooth solutions for semilinear hyperbolic systems in multi-dimensional space. In the class of piecewise smooth functions the author proves the existence and uniqueness of local solutions to the Cauehy problem for 3×3 hyperbolic system. Besides, it is also proved that when two characteristic surfaces bearing weak singularities intersect, the solution will still be piecewise smooth and the weak singularities will propagate along all characteristic surfaces.