In this paper we consider the nonlinear transmission problem for the wave equation with time dependent coefficients and nonlinear internal damping. We prove global existence and study decay properties of the solutions. The result is achieved by using the multiplier technique and suitable unique continuation theorem for the wave equation.

En este artículo consideramos el problema no lineal de transmisión para una ecuación de onda con coeficientes dependientes del tiempo y amortiguamiento interno no lineal. Se prueba la existencia global y se estudia propiedades de decaimiento de las soluciones. El resultado se alcanza usando técnicas de multiplicado res y el teorema continuación única conveniente para una ecuación de onda.

In this article we study the wave propagation over materials consisting of two components: one component is simple elastic while the other has  a nonlinear internal dampingwith elastic coefficients dependent on time; both components having source terms. Byusing the potential well method we obtain the global existence, we also show that theenergy of the system decays uniformly to zero,

In this article we study the wave propagation over materials consisting of two components: one component is simple elastic while the other has  a nonlinear internal dampingwith elastic coefficients dependent on time; both components having source terms. Byusing the potential well method we obtain the global existence, we also show that theenergy of the system decays uniformly to zero,

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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.