一类半线性双曲型方程组的柯西问题

Cauchy Problems for Second Order Systems of Semi-linear Partial Differential Equations of Hyperbolic Type

讨论一类半线性双曲型偏微分方程组的两种柯西问题,使用毕卡迭代法,获得了关于解的存在唯一性方面的结果.

A kind of semi-linear hyperbolic systems (E) are considered in this paper, we pose the first Cauchy problem (5) and the second Cauchy problem (12) to system (E), where x_0ε(α,β), y_0ε(γ,δ), x = G(y) and y = F(x). represent the same monotonic curve in R^2 with γ= F(α), δ= F(β). The existence and uniqueness of the solutions to these two problems are obtained by using the Picard iterative method.