N维空间中一类强阻尼非线性波动方程的解及其性质

A class of strongly damped nonlinear wave equation solution of N-demensional space and its properties

将强阻尼非线性波动方程在三维空间解的性质由三维推广到N(N>3)维,利用标准的Galerkin方法和Sobolev嵌入定理研究了弱解在该空间下的存在性,运用内积做出了解的耗散估计,并采用Gronwall引理证明了整体吸引子的存在性.

The properties of three dimensional space solution of strongly damped nonlinear wave equation by 3D was expanded to N dimensional space（ N 3）. A standard Galerkin method and the Sobolev embedding theorem were utilized to study the existence of weak solution under the space. The inner product was used to make the solution＇s dissipation estimates,and the Gronwall lemma was used to prove the existence of the attractor.