Estabilidade exponencial de um sistema termo elástico poroso: lei de Cattaneo versus lei de Fourier

Abstract

In this dissertation we study there rst distance and uniqueness of solutions dog as well as the exponential decay model. Our most important result concerns the exponential decay of the system porous-thermo-elasticity: utt = uxx + b x − x em (0, ) × (0, 1), J tt = xx − bux − φ + mθ − t em (0, ) × (0, 1), c t = k qx − uxt − m t em (0, ) × (0, 1), qt = 쀀 q − x em (0, ) × (0, 1), u = x = θ = q = 0 sobre (0, ) × (0, 1), (u(:, 0), (:, 0), (:, 0), q(:, 0)) = (u0(x), 0(x), 0(x), q0(x)) em (0, ), (ut(:, 0), t(:, 0)) = (u1(x), 1(x)) em (0, ), the existence and uniqueness is obtained using the Theorem of Lumer-Phillips and the expo- nential decay will use a technical the semigroup.