Topological sensitivity analysis for time-dependent problems

Boris Vexler; Takéo Takahashi; Samuel Amstutz

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Random modulation of solitons for the stochastic Korteweg–de Vries equation

A. de Bouard, A. Debussche (2007)

Annales de l'I.H.P. Analyse non linéaire

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Multiscale convergence and reiterated homogenization of parabolic problems

Anders Holmbom, Nils Svanstedt, Niklas Wellander (2005)

Applications of Mathematics

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Reiterated homogenization is studied for divergence structure parabolic problems of the form $\partial u_{ε} / \partial t - div (a (x, x / ε, x / ε^{2}, t, t / ε^{k}) \nabla u_{ε}) = f$ . It is shown that under standard assumptions on the function $a (x, y_{1}, y_{2}, t, τ)$ the sequence ${u_{ϵ}}$ of solutions converges weakly in $L^{2} (0, T; H_{0}^{1} (Ω))$ to the solution $u$ of the homogenized problem $\partial u / \partial t - div (b (x, t) \nabla u) = f$ .

A general class of phase transition models with weighted interface energy

E. Acerbi, G. Bouchitté (2008)

Annales de l'I.H.P. Analyse non linéaire

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A note on asymptotic expansion for a periodic boundary condition

Ján Filo (1998)

Archivum Mathematicum

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The aim of this contribution is to present a new result concerning asymptotic expansion of solutions of the heat equation with periodic Dirichlet–Neuman boundary conditions with the period going to zero in $3$ D.