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Un exemple concernant le comportement asymptotique de la solution bornée de l'équationd 2 u/dt 2∈∂ϕ (u)

An example concerning the asymptotic behavior of the bounded solution of the equationd 2 u/dt 2∈∂ϕ (u)

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Abstract

We prove that there exist in the Hilbert spacel 2 a lower semicontinuous convex function ϕ andu o such that the bounded and strong solutionu of the equation (d 2 u/dt 2) (t)∈∂ϕ (u(t)),t>0,u(0)=u o is weakly but not strongly convergent inl 2 ast→+∞.

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  1. Département de Mathématiques, Faculté de Sciences, Parc de Grandmont, F-37200, Tours, France

    Laurent Véron

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  1. Laurent Véron
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Véron, L. Un exemple concernant le comportement asymptotique de la solution bornée de l'équationd 2 u/dt 2∈∂ϕ (u). Monatshefte für Mathematik 89, 57–67 (1980). https://doi.org/10.1007/BF01571565

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  • DOI: https://doi.org/10.1007/BF01571565

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