Absence of nontrivial solutions for a class of partial differential equations and systems in unbounded domains.

Akrout, K.; Khodja, B.

Displaying similar documents to “Absence of nontrivial solutions for a class of partial differential equations and systems in unbounded domains.”

Corrector results for a parabolic problem with a memory effect

Patrizia Donato, Editha C. Jose (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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The aim of this paper is to provide the correctors associated to the homogenization of a parabolic problem describing the heat transfer. The results here complete the earlier study in [Jose, (2009) 189–222] on the asymptotic behaviour of a problem in a domain with two components separated by an -periodic interface. The physical model established in [Carslaw and Jaeger, The Clarendon Press, Oxford (1947)] prescribes on the interface the condition that the flux of...

Oscillations and concentrations in sequences of gradients

Martin Kružík, Agnieszka Kałamajska (2008)

ESAIM: Control, Optimisation and Calculus of Variations

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We use DiPerna’s and Majda’s generalization of Young measures to describe oscillations and concentrations in sequences of gradients, ${\nabla u_{k}}$ , bounded in $L^{p} (Ø; ℝ^{m \times n})$ if $p > 1$ and $Ω \subset ℝ^{n}$ is a bounded domain with the extension property in $W^{1, p}$ . Our main result is a characterization of those DiPerna-Majda measures which are generated by gradients of Sobolev maps satisfying the same fixed Dirichlet boundary condition. Cases where no boundary conditions nor regularity of $Ω$ are required and links with lower semicontinuity...