We prove the existence of solution for a mathematic model of diffusion of a contaminant using the Nonlinear Semigroups Theory, by means of afin operators. We also study a realistic model by means of satura tíon effects.

In this paper we show the global existence and the exponencial decay of solutions of the one-dimensional wave equation with localized frictional damping.

We proved that the semigroup C0 associated to a viscoelastic system is analytic and exponentially stable.

We prove that the eo semigroup, associated to athermoelastic system is analitic and exponential stable

In this article, we prove the existence and uniqueness of the weak solution of a nonlinear wave equation. We prove the uniqueness by using the Visik - Ladyshenkaia Method. Also, using the Nakao s Lemma, we prove the exponential decay ofthe energy associated to the system.

In this work, we consider the problem of existence of global solutions for a scalar wave equation with dissipation. We study also, the asymptotic behaviour of the solutions. In this part of the paper; we present an alternative method - inspired in nonlinear techniques. In order lo attack this problem, specifically, we used the Conrad - Rao method [l].

En este trabajo se enuncia y demuestran dos Lemas importantes de Nakao. Estos Lemas nos permitirán obtener la tasa de decaimiento de la solución de algunas ecuaciones en derivadas parciales. En particular, probamos el decaimiento exponencial de la solución global de una ecuación de onda.

Using semigroup theory we are going to prooue the global existence solution o] a evolution model, which represente the magneto-elastic waves in a boundary conduciive media. Also, we are going to prooue that the the system is well set and using Dinamic Systems and La Salle 's Invariance Principie we are going to show that the energy asociated to the system decays to zero when t→+ ∞.

Using Semigroups Theory, we prove the existence of global solution to the viscoelastic bean equation with memory, this bean is having one side fixed and the other one is provided of a control ƒ. Also, using multiplication techniques, Lyapunov functional, dynamic systems and some results of Datko, Buck, we show that the energy associated to the system decays to zero when t → + ∞, that means we get the stability of the bean.

sing monotone maximal operators Theory and the Minty-Browder theorem, we prove the existence of global solution to the elastic-dynamic system on cubic crystals, which is given a nonlinear control f. Also, using multiplicative techniques, results of R. Dautry. - J. L. Lions, integral inequalities, Russel' Principie, the W. Liu method, and adapting the F. Conrad and B. Rao method in the calculation of the estimates, we show that the energy associated to the system decays to zero when t → +∞.

In this article, we prove the exponential stability of the motion of a viscoelastic body under control, using the stabilization theory of integro differential equations, introduced by Desh

Using the notion of semigroup type, periodic solution of a nonhomogeneous equation, the fundamental principles of functional analysis, and strongly the notions of spectral theory, we give a proof of the famous and important result of Gearhart, about exponential stability of a semigroup, introduced in Liu- Zheng [1].

We prove the existence of solution for a mathematic model of diffusion of a contaminant using the Nonlinear Semigroups Theory, by means of afin operators. We also study a realistic model by means of satura tíon effects.

In this paper we show the global existence and the exponencial decay of solutions of the one-dimensional wave equation with localized frictional damping.

We proved that the semigroup C0 associated to a viscoelastic system is analytic and exponentially stable.

Se prueba que el semigrupo C0 asociado a un sistema Termoelástico es analítico y exponencialmente estable.

In this article, we prove the existence and uniqueness of the weak solution of a nonlinear wave equation. We prove the uniqueness by using the Visik - Ladyshenkaia Method. Also, using the Nakao s Lemma, we prove the exponential decay ofthe energy associated to the system.

En este trabajo consideramos el problema de existencia de soluciones globales para la ecuación escalar de la onda con disipación. Estudiamos también el comportamiento asintótico de las soluciones, y presentamos un método alternativo inspirado en técnicas no lineales; específicamente usamos el método de Conrad-Rao [1].

En este trabajo se enuncia y demuestran dos Lemas importantes de Nakao. Estos Lemas nos permitirán obtener la tasa de decaimiento de la solución de algunas ecuaciones en derivadas parciales. En particular, probamos el decaimiento exponencial de la solución global de una ecuación de onda.

Using semigroup theory we are going to prooue the global existence solution o] a evolution model, which represente the magneto-elastic waves in a boundary conduciive media. Also, we are going to prooue that the the system is well set and using Dinamic Systems and La Salle 's Invariance Principie we are going to show that the energy asociated to the system decays to zero when t→+ ∞.