一类半线性双曲方程的Cauchy问题

The Cauchy Problem for some Class of Semilinear Hyperbolic Differential Equations

讨论推广了一类具有非线性项的 Euler-Poisson-Darboux 方程的 Cauchy 问题可解性及大范围解的存在性.利用线性方程 Cauchy 问题的整体可解性及逐步迭代法,通过先验估计证明了所得出的一系列解按 L^2-范数收敛,且该收敛函数就是所讨论问题的唯一强解.并利用高阶能量估计得到该问题古典解存在.

The main aim is to study the soluble and the existence of global solution for the Cauchy proplem of generalized Euler-Poisson-Darboux's equations with nonlinear terms.According to the existence of the global solution of the Cauchy problem of the linearized equations and the iterative method,the sequence of solutions is obtained and it is proved by means of priori estimates that the sequence converges to some function in L^2norm which is the unique strong solution of the above problem.And by the higher prori estimates,the classical solution is obtained.