Displaying similar documents to “Mathematical and numerical analysis of a stratigraphic model”

Homogenization of ferromagnetic multilayers in the presence of surface energies

Kévin Santugini-Repiquet (2007)

ESAIM: Control, Optimisation and Calculus of Variations

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We study the homogenization process of ferromagnetic multilayers in the presence of surface energies: super-exchange, also called interlayer exchange coupling, and surface anisotropy. The two main difficulties are the non-linearity of the Landau-Lifshitz equation and the absence of a good sequence of extension operators for the multilayer geometry. First, we consider the case when surface anisotropy is the dominant term, then the case when the magnitude of the super-exchange interaction...

Renormalized solution for nonlinear degenerate problems in the whole space

Mohamed Maliki, Adama Ouedraogo (2008)

Annales de la faculté des sciences de Toulouse Mathématiques

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We consider the general degenerate parabolic equation : u t - Δ b ( u ) + d i v F ˜ ( u ) = f in Q = ] 0 , T [ × ℝ N , T > 0 . We suppose that the flux F ˜ is continuous, b is nondecreasing continuous and both functions are not necessarily Lipschitz. We prove the existence of the renormalized solution of the associated Cauchy problem for L 1 initial data and source term. We establish the uniqueness of this type of solution under a structure condition F ˜ ( r ) = F ( b ( r ) ) and an assumption on the modulus of continuity of b . The novelty of this work is...

Conditions of Prodi-Serrin's type for local regularity of suitable weak solutions to the Navier-Stokes equations

Zdeněk Skalák (2002)

Commentationes Mathematicae Universitatis Carolinae

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In the context of suitable weak solutions to the Navier-Stokes equations we present local conditions of Prodi-Serrin’s type on velocity 𝐯 and pressure p under which ( 𝐱 0 , t 0 ) ∈ Ω × ( 0 , T ) is a regular point of 𝐯 . The conditions are imposed exclusively on the outside of a sufficiently narrow space-time paraboloid with the vertex ( 𝐱 0 , t 0 ) and the axis parallel with the t -axis.