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Arrieta, M. and Carvalho, A.N. (2000) Abstract Parabolic Problems with Critical Nonlinearities and Applications to Navier-Stokes and Heat Equations. Transactions of the American Mathematical Society, 352, 285-310.
http://dx.doi.org/10.1090/S0002-9947-99-02528-3

has been cited by the following article:

• 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.