Spatial ceasing and decay of solutions to nonlinear hyperbolic equations with nonlinear boundary conditions

摘要

In this work we study the spatial behavior of solutions to some nonlinear hyperbolic equations with nonlinear boundary conditions. Under suitable conditions, by using the weighted energy method, we prove that the solutions either cease to exist for a finite value of the spatial variable or decay algebraically in the spatial variable. (C) 2008 Elsevier Ltd. All rights reserved.