带低正则外力项的分数次阻尼波方程的长时间行为

ON THE LONG-TERM BEHAVIOR OF FRACTIONAL DAMPED WAVE EQUATION WITH LOW REGULAR FORCE TERM

本文主要考虑三维空间中有界区域上带低正则外力项的分数次阻尼波方程的长时间行为.利用分数次拉普拉斯算子生成的算子半群的解析性,我们改进了分数次阻尼波方程Strichartz估计.由于超临界非线性下波方程的弱解唯一性无法验证,为了克服这个困难,我们对弱解增加了适当的限制条件,考虑了平移正则解.然后证明了平移正则解的适定性.进一步得到了全局吸引子的存在性.

The purpose of this work is to consider long-term behavior of the fractional damped wave equation with low regular force term on the bounded domain of.Firstly,we improve the Strichartz inequality of linear equation via considering the analyticity of operator semigroup generated by fractional Laplacian.Then,we obtain the well-posedness of translational regular solutions,and existence of global attractors.