En régulatrité maximale des equations d'order 2 dans l'espace de Hilbert.
Language
en
Document de travail - Pré-publication
English Abstract
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 ...Read more >
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.Read less <
English Keywords
Damped wave equation
maximal regularity
non-autonomous evolution equations Mathematics Subject Classification (2010): 35K90
35K45
47D06
Origin
Hal imported