Author(s)

Qinghua Zhang

Department of Mathematics, Nantong University, Nantong, China.

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.

Negative Laplacian, Wave Equation, Strong Damping, Sectorial Operator, Fractional Power, Global Attractor

Zhang, Q. (2016) On the Strongly Damped Wave Equations with Critical Nonlinearities. Journal of Applied Mathematics and Physics, 4, 697-705. doi: 10.4236/jamp.2016.44080.