Asymptotic dynamics of wave equations on compact Riemannian manifolds: sharp localized damping and supercritical forcing

• Ano de defesa: 2019
• Autor(a) principal: Huertas, Paulo Nicanor Seminario
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Amortecimento não linear localizado; Atratores globais; Equações da onda Riemannianas; Global attractors; Nonlinear localized damping; Riemannian wave equations
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/55/55135/tde-24102022-111718/

The present thesis is concerned with long-time dynamics of wave equations, defined on compact Riemannian manifolds, with boundary, and featuring localized damping and nonlinear forcing terms with supercritical Sobolev growth. The main objective is to construct optimal damping regions with arbitrarily small summed interior/boundary measure that imply the existence of a regular finite-dimensional global attractor. To this end, among other results, we prove a supercritical extension of a unique continuation theorem of Triggiani and Yao (2002).