Comportamento assintótico para uma equação do tipo Moore-Gibson-Thompson

• Autor(a) principal: Arthur Henrique Caixeta
• Data de Publicação: 2016
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Repositório Institucional da Universidade Estadual de Maringá (RI-UEM)
• Texto Completo: http://repositorio.uem.br:8080/jspui/handle/1/5528
• topic: Análise matemática; Moore-Gibson-Thompson - Equação de; Acústica não linear; Sistemas dinâmicos (Matemática); Teoria assintótica; Third Order Equation; Moore-Gibson-Thompson Equation; Global attractor; Ciências Exatas e da Terra; Matemática

Long-time behavior of the Moore-Gibson-Thompson equation (MGT) is considered. This type of equations arises in the context of nonlinear acoustics [10, 21, 17] where modeling accounts for a finite speed of propagation paradox, the latter results in hyperbolic nature of the dynamics. At first, we will prove that the third order equation in consideration generates a well-posed dynamical system which admits a global and finite dimensional attractor. The main difficulty associated with the problem is the lack of Lyapunov function along with the lack of compactness of trajectories, which fact prevents applicability of standard tools in the area of dynamical systems. The second approach considers the MGT equation subjected to viscoelastic effects. Obtaining uniform exponential decay rate is linked with usual restrictive assumptions regarding the function that localizes the frictional damping