Initial-boundary Problems For Semilinear Hyperbolic Systems With Strongly Singular Initial Data

There are many problems in physics and some other nature sciences can be de-scribed by first order hyperbolic systems, such as the motion of elasticity, gas dynamicsetc. In practice, behaviors of pluses and highly oscillatory waves can be characterizedwith waves which have some kinds of strong singularities such as the delta functionsand their derivatives. Therefore it is necessary to study initial-boundary value prob-lems of partial differential equations with strongly singular initial data. However, asthere are some strong singularities in initial data, in general, we can not discuss theseproblems in classical solution spaces.In this paper, we study the initial-boundary problems of first order semilinearhyperbolic systems which have strongly singular initial data by the approach of regu-larization approximation. We consider the propagation and reffection of singularities.Under certain restriction of singularities and the growth rate of the nonlinear items weget that the asymptotic behavior of solutions satisfies the so-called nonlinear super-...