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Document Type: Dissertação
Title: Well-posedness and regularity theory for abstract integrodifferential equations in interpolation scales and applications
Authors: Santana, Marcos Gabriel de
Issue Date: 26-Feb-2021
Advisor: Santos, Bruno Luis de Andrade
Resumo : In this work, we study the initial value problem associated with the abstract integrodifferential equation u'(t) = S g(t − s)Au(s)ds + f(t, u(t)), t > 0, with critical or subcritical nonlinearity f in interpolation scales. We prove local-in-time existence, uniqueness, continuation, and blow-up alternative of the E-regular solution that satisfies a specific condition of controlled behavior at t = 0. Then, we apply the theory to the Navier-Stokes problem with hereditary viscosity and initial data in the scale of fractional power spaces associated with the Stokes operator; and to reaction-diffusion problems with super-linear and gradient nonlinearities, and initial data in Lebesgue and Besov spaces, respectively.
Keywords: Matemática
Equações diferenciais não-lineares
Equações de Navier-Stokes
Integrodifferential equations
Critical nonlinearities
Local well-posedness
Continuation and blow-up alternative
Regularity theory
Navier-Stokes with hereditary viscosity
Reaction-diffusion with memory
Sponsorship: Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
Language: eng
Institution: Universidade Federal de Sergipe
Program Affiliation: Pós-Graduação em Matemática
Citation: SANTANA, Marcos Gabriel de. Well-posedness and regularity theory for abstract integrodifferential equations in interpolation scales and applications. 2021. 107 f. Dissertação (Mestrado em Matemática) – Universidade Federal de Sergipe, São Cristóvão, 2021.
Appears in Collections:Mestrado em Matemática

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