Estabilização uniforme da equação da onda sobre uma superfície compacta com dissipação localmente distribuída - Cesar Augusto Bortot (2011)
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.