Soluções exatas para a equação de Fokker-Planck não-linear

• Ano de defesa: 2004
• Autor(a) principal: Ichiba, Claudio
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Estadual de Maringá; Brasil; Programa de Pós-Graduação em Física; UEM; Maringá, PR; Departamento de Física
• Palavras-chave em Português: Equação de Fokker-Planck; Exponencial "q" de Tsallis; Oscilador harmônico; Ansatz gaussiano.; Ciências Exatas e da Terra; Física
• Link de acesso: http://repositorio.uem.br:8080/jspui/handle/1/2733

A study about the anomalous diffusion employing a non-linear Fokker-Planck equation is developed here. Exact solutions with time and space dependence were found from a generalized gaussian ansatz based on Tsallis q-exponential. This was done in cases without external force, with constant and linear external forces, and with a source term. Also, time independent (stationary) solutions were obtained. The solutions with long tail, found via the generalized gaussian ansatz, have power laws as asymptotic behavior. These power laws are exact solutions too. In this last context a family of symmetrical anarmonic oscillators, that has as particular cases the harmonic oscillator and the infinite square well, was investigated. An ansatz that contains as special cases the power law and generalized gaussian was also considered.