ARENDT, Wolfgang; DIER, Dominik; LAASRI, Hafida; OUHABAZ, El Maati

Métadonnées

Afficher la notice complète

Licence d’utilisation du document

ARENDT, Wolfgang
Insttiut for applied analysis

DIER, Dominik
Insttiut for applied analysis

LAASRI, Hafida
Département de Mathématiques

Langue

Article de revue

Ce document a été publié dans

Advances in Differential Equations. 2014p. ???

Khayyam Publishing

Résumé en anglais

\begin{abstract}\label{abstract} We consider a non-autonomous evolutionary problem \[ \dot{u} (t)+\A(t)u(t)=f(t), \quad u(0)=u_0 \] where the operator $\A(t):V\to V^\prime$ is associated with a form $\fra(t,.,.):V\times V \to \R$ and $u_0\in V$. Our main concern is to prove well-posedness with maximal regularity which means the following. Given a Hilbert space $H$ such that $V$ is continuously and densely embedded into $H$ and given $f\in L^2(0,T;H)$ we are interested in solutions $u \in H^1(0,T;H)\cap L^2(0,T;V)$. We do prove well-posedness in this sense whenever the form is piecewise Lipschitz-continuous and symmetric. Moreover, we show that each solution is in $C([0,T];V)$. We apply the results to non-autonomous Robin-boundary conditions and also use maximal regularity to solve a quasilinear problem.< Réduire

Mots clés en anglais

Sesquilinear forms

non-autonomous evolution equations

maximal regularity

non-linear heat equations

URI

https://oskar-bordeaux.fr/handle/20.500.12278/189290

Project ANR

Aux frontières de l'analyse Harmonique - ANR-12-BS01-0013

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251