Analyse numérique de problèmes non convexes à donnée au bord non linéaire

Abstract : In this thesis, we study a kind of non-convex varaitional problems. Such problems originated in material science, for example in crystal, etc. We consider the following problems : inf#(*(x)) dx; inf#(*(x))+((x)a(x)) dx on certain Sobolev space w#1#p(a) and where the energy density posses energy wells, say w1 i=1,...k. In general, such problems can be no classical solution. In our studies, the numerical method introduced by M. Chipot, C. Collins and D. Kinderlerer has been developped. In section 1 and 2 some results of estimation in a space of finit-element are obtained. Section 3 is contributed to an analysis or parametrized measure. We get a result of Young measure which showing the existence and uniqueness of the generalized solution. And in section 4, we have some estimation results in terms of probability, which explains the behavior of the minimising sequences
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Wei Li. Analyse numérique de problèmes non convexes à donnée au bord non linéaire. Mathématiques générales [math.GM]. Université Paul Verlaine - Metz, 1993. Français. ⟨NNT : 1993METZ010S⟩. ⟨tel-01775433⟩

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