SPATIAL BEHAVIOR OF SOLUTIONS FOR A CLASS OF HYPERBOLIC EQUATIONS WITH NONLINEAR DISSIPATIVE TERMS

Abstract

This paper deals with the spatial behavior of solutions for aviscoelastic wave equations with nonlinear dissipative terms in asemi-infinite $n$-dimensional cylindrical domain. An alternativeof Phragm\'{e}n-Lindel\"{o}f type theorems is obtained in theresult. In the case of decay, an upper bound will be derived forthe total energy by means of the boundary data. The main point ofthe contribution is the use of energy method.