带有临界型非线性项的强阻尼波动方程

Strongly Damped Wave Equations with Critical Nonlinearities

研究一类带有临界型非线性项的强阻尼波动方程.通过选择合适的状态空间,证明了算子矩阵[OA-IηAθ]的扇形性,评估了带有临界型增长指数的非线性项的临界性,并且研究了弱解的局部与整体存在性和正则性.

We study the strongly damped wave equations with critical nonlinearities.By choosing suitable state spaces,we prove sectorial properties of the operator matrix[OA-IηAθ],analysis the criticality of the nonlinearities with critical growth,and investigate the local and global existence of weak solutions together with their higher regularity.