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Homogenization of Neumann problems for unbounded integral functionals

Luciano Carbone, Antonio Corbo Esposito, Riccardo De Arcangelis (1999)

Bollettino dell'Unione Matematica Italiana

Si studia l'omogeneizzazione di problemi di tipo Neumann per funzionali integrali del Calcolo delle Variazioni definiti su funzioni soggette a vincoli puntuali di tipo oscillante sul gradiente, in ipotesi minimali sui vincoli. I risultati ottenuti sono dedotti mediante l'introduzione di nuove tecniche di Γ -convergenza, unitamente ad un risultato di ricostruzione per funzioni affini a tratti, che permettono la dimostrazione di un teorema generale di omogeneizzazione per funzionali integrali a valori...

Homogenization of parabolic equations an alternative approach and some corrector-type results

Anders Holmbom (1997)

Applications of Mathematics

We extend and complete some quite recent results by Nguetseng [Ngu1] and Allaire [All3] concerning two-scale convergence. In particular, a compactness result for a certain class of parameterdependent functions is proved and applied to perform an alternative homogenization procedure for linear parabolic equations with coefficients oscillating in both their space and time variables. For different speeds of oscillation in the time variable, this results in three cases. Further, we prove some corrector-type...

Homogenization of periodic non self-adjoint problems with large drift and potential

Grégoire Allaire, Rafael Orive (2007)

ESAIM: Control, Optimisation and Calculus of Variations

We consider the homogenization of both the parabolic and eigenvalue problems for a singularly perturbed convection-diffusion equation in a periodic medium. All coefficients of the equation may vary both on the macroscopic scale and on the periodic microscopic scale. Denoting by ε the period, the potential or zero-order term is scaled as ε - 2 and the drift or first-order term is scaled as ε - 1 . Under a structural hypothesis on the first cell eigenvalue, which is assumed to admit a unique minimum in the...

Homogenization of periodic nonconvex integral functionals in terms of Young measures

Omar Anza Hafsa, Jean-Philippe Mandallena, Gérard Michaille (2006)

ESAIM: Control, Optimisation and Calculus of Variations

Homogenization of periodic functionals, whose integrands possess possibly multi-well structure, is treated in terms of Young measures. More precisely, we characterize the Γ -limit of sequences of such functionals in the set of Young measures, extending the relaxation theorem of Kinderlherer and Pedregal. We also make precise the relationship between our homogenized density and the classical one.

Homogenization of periodic nonconvex integral functionals in terms of Young measures

Omar Anza Hafsa, Jean-Philippe Mandallena, Gérard Michaille (2005)

ESAIM: Control, Optimisation and Calculus of Variations

Homogenization of periodic functionals, whose integrands possess possibly multi-well structure, is treated in terms of Young measures. More precisely, we characterize the Γ-limit of sequences of such functionals in the set of Young measures, extending the relaxation theorem of Kinderlherer and Pedregal. We also make precise the relationship between our homogenized density and the classical one.

Homogenization of periodic semilinear hypoelliptic PDEs

Alassane Diédhiou, Étienne Pardoux (2007)

Annales de la faculté des sciences de Toulouse Mathématiques

We establish homogenization results for both linear and semilinear partial differential equations of parabolic type, when the linear second order PDE operator satisfies a hypoellipticity asumption, rather than the usual ellipticity condition. Our method of proof is essentially probabilistic.

Homogenization of quadratic complementary energies: a duality example

Hélia Serrano (2011)

Mathematica Bohemica

We study an example in two dimensions of a sequence of quadratic functionals whose limit energy density, in the sense of Γ -convergence, may be characterized as the dual function of the limit energy density of the sequence of their dual functionals. In this special case, Γ -convergence is indeed stable under the dual operator. If we perturb such quadratic functionals with linear terms this statement is no longer true.

Homogenization of quasilinear optimal control problems involving a thick multilevel junction of type 3 : 2 : 1

Tiziana Durante, Taras A. Mel’nyk (2012)

ESAIM: Control, Optimisation and Calculus of Variations

We consider quasilinear optimal control problems involving a thick two-level junction Ωε which consists of the junction body Ω0 and a large number of thin cylinders with the cross-section of order 𝒪(ε2). The thin cylinders are divided into two levels depending on the geometrical characteristics, the quasilinear boundary conditions and controls given on their lateral surfaces and bases respectively. In addition, the quasilinear boundary conditions depend on parameters ε, α, β and the...

Homogenization of quasilinear optimal control problems involving a thick multilevel junction of type 3 : 2 : 1∗

Tiziana Durante, Taras A. Mel’nyk (2012)

ESAIM: Control, Optimisation and Calculus of Variations

We consider quasilinear optimal control problems involving a thick two-level junction Ωε which consists of the junction body Ω0 and a large number of thin cylinders with the cross-section of order 𝒪(ε2). The thin cylinders are divided into two levels depending on the geometrical characteristics, the quasilinear boundary conditions and controls given on their lateral surfaces and bases respectively. In addition, the quasilinear boundary...

Homogenization of quasilinear optimal control problems involving a thick multilevel junction of type 3 : 2 : 1∗

Tiziana Durante, Taras A. Mel’nyk (2012)

ESAIM: Control, Optimisation and Calculus of Variations

We consider quasilinear optimal control problems involving a thick two-level junction Ωε which consists of the junction body Ω0 and a large number of thin cylinders with the cross-section of order 𝒪(ε2). The thin cylinders are divided into two levels depending on the geometrical characteristics, the quasilinear boundary conditions and controls given on their lateral surfaces and bases respectively. In addition, the quasilinear boundary...

Homogenization of quasilinear parabolic problems by the method of Rothe and two scale convergence

Emmanuel Kwame Essel, Komil Kuliev, Gulchehra Kulieva, Lars-Erik Persson (2010)

Applications of Mathematics

We consider a quasilinear parabolic problem with time dependent coefficients oscillating rapidly in the space variable. The existence and uniqueness results are proved by using Rothe’s method combined with the technique of two-scale convergence. Moreover, we derive a concrete homogenization algorithm for giving a unique and computable approximation of the solution.

Currently displaying 261 – 280 of 393