一类具有粘弹性项和非线性边界耗散的波动方程解的存在唯一性

Existence and Uniqueness of Solution for a Class of Wave Equations with Viscoelastic Term and Nonlinear Boundary Dissipation

讨论一类具有粘弹性项和非线性Neumann边界耗散的波动方程解的存在唯一性.首先利用极大单调算子理论,建立在有限时间区域内解的存在唯一性.然后利用解的能量估计得到全局解.

In this paper,we discuss the existence and uniqueness of solution for a class of wave equations with viscoelastic term and nonlinear Neumann boundary dissipation.First,we establish the existence and uniqueness of solution on a finite time interval with the maximal monotone operator theory.Then,using the energy estimation of the solution,we obtain the global solution.