Decay estimates of solutions of a nonlinearly damped semilinear wave equation
Volume 85 / 2005
Annales Polonici Mathematici 85 (2005), 25-36
MSC: 35B40, 35L55, 35B37.
DOI: 10.4064/ap85-1-3
Abstract
We consider an initial boundary value problem for the equation $u_{tt}-{\mit \Delta } u-\nabla \phi \cdot \nabla u+f(u)+g(u_{t})=0$. We first prove local and global existence results under suitable conditions on $f$ and $g$. Then we show that weak solutions decay either algebraically or exponentially depending on the rate of growth of $g$. This result improves and includes earlier decay results established by the authors.
