TITLE:
On the Strongly Damped Wave Equations with Critical Nonlinearities
AUTHORS:
Qinghua Zhang
KEYWORDS:
Negative Laplacian, Wave Equation, Strong Damping, Sectorial Operator, Fractional Power, Global Attractor
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.4 No.4,
April
26,
2016
ABSTRACT: We study the strongly damped wave equations with critical nonlinearities. By choosing suitable state spaces, we prove sectorial property of the operator matrix together with its adjoint operator, investigate the associated interpolation and extrapolation spaces, analysis the criticality of the nonlinearity with critical growth, and study the higher spatial regularity of the Y-regular solution by bootstrapping.