Global existence of the $\epsilon$-regular solution for the strongly damping wave equation

• Main Author: Qinghua Zhang
• Format: Article
• Language: English
• Published: University of Szeged 2013-11-01
• Series: Electronic Journal of Qualitative Theory of Differential Equations
• Subjects: negative laplacian; wave equation; strong damping; sectorial operator; fractional power; interpolation and extrapolation spaces; criticality; $\varepsilon$-regular solution; global existence
• Online Access: http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=2270

In this paper, we deal with the semilinear wave equation with strong damping. By choosing a suitable state space, we characterize the interpolation and extrapolation spaces of the operator matrix $\mathbf{A}_{\theta}$, analysis the criticality of the $\varepsilon$-regular nonlinearity with critical growth. Finally, we investigate the global existence of the $\varepsilon$-regular solutions which have bounded $X^{1/2}\times X$ norms on their existence intervals.