一类拟线性双曲型方程的初值问题

基于双曲型线性偏微分算子理论，引入并研究了具有非零初始值的拟线性双曲型方程的定解问题．由速降函数空间上的傅立叶变换的内积得到了相应的希尔伯特空间和一个重要的估计式．在已知函数满足某些假设条件时，利用Schauder不动点定理证明了该初值问题解的存在性定理．

Initial Value Problem of Quasi-linear Hyperbolic Equations

Based on theory of hyperbolic linear partial differential operator, the initial value problem of a kind of quasi-linear hyperbolic equations with non-zero initial values was introduced and studied. The Hilbert space and an important inequality were obtained using interior product of the Fourier transform on a quickly decaying functional space. The existence theorem of the solutions for the initial value problem was proved using Schauder fixed-point theorem under some assumed conditions of known function.