Estabilização uniforme da equação da onda sobre uma superfície compacta com dissipação localmente distribuída

Abstract

This work is concerned with the study of wave equation on compact surfaces and locally distributed damping, described by utt − ∆Mu + a(x)g(ut) = 0 em M × (0,∞) u(x, 0) = u 0 (x) , u0 (x, 0) = u 1 (x) where M ⊂ R 3 is a smooth (of class C 3 ) oriented embedded compact surface without boundary, such that M = M0 ∪ M1, where M1 = {x ∈ M; m(x) · ν(x) > 0} and M0 = M \M1, here, m(x) := x − x 0 , x 0 ∈ R 3 , and ν is the exterior unit normal vector field of M.