En régulatrité maximale des equations d'order 2 dans l'espace de Hilbert.

ACHACHE, Mahdi

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ACHACHE, Mahdi
Institut de Mathématiques de Bordeaux [IMB]

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Document de travail - Pré-publication

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We consider the problem of maximal regularity for semilinear non-autonomous second order Cauchy problems    u ′′ (t) + B(t)u ′ (t) + A(t)u(t) = F (t, u, u ′) t-a.e. u(0) = u 0 , u ′ (0) = u 1. (0.1) Here, the time dependent operator A(t) is bounded from the Hilbert space V to its dual space V ′ and B(t) is associated with a sesquilinear form b(t, ·, ·) with domain V. We prove maximal L 2-regularity results and other regularity properties for the solutions of the above equation under minimal regularity assumptions on the operators and the inhomogeneous term F. One of our main results shows that maximal L 2-regularity holds if the operators are piecewise H 1 2 with respect to t. This regularity assumption is optimal and provides the best positive result on this problem.< Leer menos

Palabras clave en inglés

Damped wave equation

maximal regularity

non-autonomous evolution equations Mathematics Subject Classification (2010): 35K90

35K45

47D06

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