ISSN:
0219-175X
Keywords:
Galerkin approximation
;
uniform decay
;
non-linear boundary conditions
;
potentials
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract In this paper, we study a hyperbolic model based on the equation $$y_{tt}-\Delta_{y} + \sum_{j = 1}^{n}b_j(x,t)\frac{\partial y_{t}}{\partial x_j}= 0 $$ with nonlinear boundary conditions given by $$\frac{\partial y}{\partial v}+ f(y) + g(y_t)= 0$$ . We prove the existence and the uniqueness of global solutions. Also, we obtain the uniform decay of the energy without control of its derivative sign.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s10012-000-0183-6