半线性双曲型方程的强间断初值问题

Initial value problem for semilinear hyperbolic equations with discontinuous data

探讨了半线性二阶变系数严格双曲型方程的强间断初值问题 ,提出局部展平特征曲面 ,获得方程的二阶项信息 ,建立先验估计的方法 ,并应用所得的先验估计证明了强间断解的局部存在性和唯一性 ,同时给出间断解的强奇性结构 。

This paper is concerned with the initial value problem for semilinear strictly hyperbolic second-order equations with discotinuous data, we presents a new method of establishing prior estimates, proves the local existence theorem of discontinuous solution and obtain the structure of singularities of the solution.