EXISTENCIA GLOBAL Y COMPORTAMIENTO ASINTÓTICO PARA UNA ECUACIÓN DE KIRCHOFF CON TÉRMINO DISIPATIVO DE COEFICIENTE VARIABLE

Consideramos una ecuación de onda no lineal, con un término disipativo del tipo a(x)u' (el Coeficiente a depende de la variable espacial). Usando el método de FAEDO-GALERKIN, y definiendo funcionales, de energía adecuados, encontraremos existencia global de la solución para datos pequeños. Una vez hecho esto usamos desigualdades integrales para mostrar que la energía del sistema decae a cero de manera exponencial

A perturbed elliptic problem involving the p(x)-Kirchhoff type triharmonic operator

This paper examines the existence of weak solutions for a nonlinear boundary value problem of p(x)-Kirchhoff type involving the p(x)-Kirchhoff type triharmonic operator and perturbed external source terms. We establish our results by using a Fredholm-type result for a couple of nonlinear operators, in the framework of variable exponent Sobolev spaces

NULL CONTROLLABILITY FOR THE SEMILINEAR HEAT EQUATION IN UNBOUNDED DOMAINS

In this paper, we consider the null controllability problem for the semilinear heat equation in an unbounded domain Ω of RN with Dirichlet boundary conditions. The control ís assumed to be distributed along a subdomain w such that the uncontrolled regian Ω\w ís bounded. Using Carleman inequalities we first prove the null controllabitity of the linearized equation. Then, by a fixed point method, we obtain the main result for the semilinear case. This result asserts that, when the nonlinearity is globally Lipschitz, the system is null controllable

THE NON LINEAR TRANSMISSION PROBLEM WITH TIME DEPENDENT COEFFICIENTS

In this paper we consider the nonlinear transmission problem for the wave equation with time dependent coefficients and linear internal damping. We prove global existence and exponential decay of solution. The result is achieved by considering energy like - Lyapunov functionals and suitable unique continuation theorem for the wave equation

GLOBAL EXISTENCE OF SOLUTIONS FOR THE DEGENERATE WAVE EQUATIONS OF KIRCHOFF TYPE WITH NONLINEAR DISSIPATIVE TERM OF VARIABLE COEFFICIENT

In this paper we investigate the global existence and decay of solutions to a degenerate wave equations with nonlinear dissipative term of variable coefficient

OBSERVACIONES SOBRE LA EXISTENCIA GLOBAL DE LAS SOLUCIONES DE UNA ECUACION DE KIRCHOFF NO LINEAL VIA EL METODO DE TARTAR

En el presente trabajo investigamos la existencia global de las soluciones de una Ecuación no Lineal, prescindiendo del "Potential well Method" y aplicamos el método del Tarta

EXISTENCIA GLOBAL Y DECAIMIENTO DE LA ENERGÍA DE UNA ECUACIÓN DE KIRCHOFF CON DISIPACIÓN LOCALIZADA

En este trabajo estudiamos la existencia y unicidad de la solución global de la ecuación de Kirchoff .... Con una disipación au' y demostraremos el decaimiento exponencial de su energía