On the Existence and the Uniform Decay of a Hyperbolic Equation with Non-Linear Boundary Conditions期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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On the Existence and the Uniform Decay of a Hyperbolic Equation with Non-Linear Boundary Conditions

Authors:	M M Cavalcanti V N Domingos Cavalcanti J A Soriano L A Medeiros

Institution:	(1) Department of Mathematics, University Estadual de Maringá, 87020-900 Maringá-PR, Brazil;(2) Instituto de Matemática, UFRJ, CP. 68530, 21945-970 Rio de Janeiro, Brazil

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.AMS Subject Classification (2000), 35L05, 35L70, 35B40

Keywords:	Galerkin approximation uniform decay non-linear boundary conditions potentials
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