一类拟线性波动方程整体强解的存在唯一性

Existence and Uniqueness of the Global Strong Solution to a Class of Quasi-linear Wave Equation

为了研究物体的波动等应用领域中的一类带有粘性项和非线性扰动项的拟线性波动方程初边值问题,在假设粘性效应系数属于一次连续可导函数,外力及初始函数满足一定条件的情况下,利用Galerkin方法证明了该问题的整体强解的存在性,运用Gronwall不等式证明了解的唯一性,进一步推广了Preste的结果。

This paper mainly investigates the initial boundary value problem for a class of quasi-linear wave equations with a viscosity and a nonlinear perturbation.Suppose that the coefficient of the nonlinear strong dissipation belongs to first order continuously differentiable function,the force and initial function that satisfy certain conditions,the existence and uniqueness of the global strong solution to the equation is obtained by using the Galerkin method and the Gronwall inequality,which extends the result of Preste.