具耗散项非线性波动方程解的正则性分析

The Regularity Analysis of the Solutions to a Class of Nonlinear Wave Equations with Dissipation

研究一类具耗散项非线性波动方程整体解的存在性,借助偏微分方程的一些标准技巧对非线性项进行估计,利用嵌入定理和算子半群的方法证明了在相对较弱的条件下上述问题整体解的存在性,并对解的正则性进行了分析.

In this paper,the existence of the global solutions to a class of nonlinear wave equations with dissipation is studied. By some standard methods,the non-linear terms are estimated. Using embedding theorem and the method of semigroup,the existence of the global solutions for the above-mentioned problem is obtained. And the regularity of the solutions is analyzed.