In this paper we are concerned with the stability of solutions for the wave equation with a viscoelastic Boundary condition and source term by using the potential well method, the multiplier technique and unique continuation theorem for the wave equation with variable coefficient.

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En este artículo estamos interesados en la estabilidad de las soluciones de una ecuación de onda con una condición de frontera viscoelástica y un término fuente, usaremos el método potencial, la técnica de multiplicadores y el teorema de unicidad para una ecuación de onda con coeficientes variables.

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In this work we are concerned with the existence of strong solutions and exponential decay of the total energy for the initial boundary value problem associated with the quasilinear wave equation with nonlinear source and boundary damping term. The results are proved by means of the potential well method, the multiplier technique and suitable unique continuation theorem for the wave equation with the variable coefficient.

En este trabajo estamos interesados con la existencia de soluciones fuertes y decaimiento exponencial de la energía total para el problema de valores iniciales en la frontera asociado a la ecuación de onda con término fuente no lineal y amortiguación en la frontera. Los resultados son probados en términos del método potencial, la técnica de multiplicación y el conveniente teorema de única continuación para la ecuación de onda con coeficientes variables.

In this work we are concerned with the existence of strong solutions andexponential decay of the total energy for the initial boundary value problem associatedwith the quasilinear wave equation with nonlinear source, under the assumption thatthe velocity boundary feedback is dissipative. The results are proved by means ofthe potential well method, the multiplier technique and suitable unique continuationtheorem for the wave equation with variable coefficients.

In this work we are concerned with the existence of strong solutions andexponential decay of the total energy for the initial boundary value problem associatedwith the quasilinear wave equation with nonlinear source, under the assumption thatthe velocity boundary feedback is dissipative. The results are proved by means ofthe potential well method, the multiplier technique and suitable unique continuationtheorem for the wave equation with variable coefficients.

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We evalúate the uniform decay of the energy associated with a model semi lineal plates, with dissipation distributed locally, using the principle of continuation single result studied by Ruiz [9] and applied to work with locallydistributed by Zuazua dissipation [10].

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Se estudia el decaimiento uniforme de la energía asociada a un modelode placas semilineal, con disipación localmente distribuido, empleando el principio de la continuación única, estudiado por Ruiz [9] y aplicados a trabajos con disipación localmente distribuida por Zuazua [10].