Displaying similar documents to “Continuous dependence for the pseudoparabolic equation.”

An existence theorem for the Boussinesq equations with non-Dirichlet boundary conditions

Zdeněk Skalák, Petr Kučera (2000)

Applications of Mathematics

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The evolution Boussinesq equations describe the evolution of the temperature and velocity fields of viscous incompressible Newtonian fluids. Very often, they are a reasonable model to render relevant phenomena of flows in which the thermal effects play an essential role. In the paper we prescribe non-Dirichlet boundary conditions on a part of the boundary and prove the existence and uniqueness of solutions to the Boussinesq equations on a (short) time interval. The length of the time...

Estimates of weighted Hölder norms of the solutions to a parabolic boundary value problem in an initially degenerate domain

Antonio Fasano, Vsevolod Solonnikov (2002)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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A-priori estimates in weighted Hölder norms are obtained for the solutions of a one- dimensional boundary value problem for the heat equation in a domain degenerating at time t = 0 and with boundary data involving simultaneously the first order time derivative and the spatial gradient.