DIER, Dominik; OUHABAZ, El Maati

doi:10.1007/s00020-013-2109-6

Metadatos

Mostrar el registro completo del ítem

Licencia de uso del documento

DIER, Dominik
Insttiut for applied analysis

OUHABAZ, El Maati
Institut de Mathématiques de Bordeaux [IMB]

Idioma

Article de revue

Este ítem está publicado en

Integr. Eqs and Op. Theory. 2014, vol. 78, n° 3, p. 427-450

Resumen en inglés

We consider non-autonomous wave equations \[ \left\{ \begin{aligned} &\ddot u(t) + \B(t)\dot u(t) + \A(t)u(t) = f(t) \quad t\text{-a.e.}\\ &u(0)=u_0,\, \dot u(0) = u_1. \end{aligned} \right. \] where the operators $\A(t)$ and $\B(t)$ are associated with time-dependent sesquilinear forms $\fra(t,.,.)$ and $\frb$ defined on a Hilbert space $H$ with the same domain $V$. The initial values satisfy $ u_0 \in V$ and $u_1 \in H$. We prove well-posedness and maximal regularity for the solution both in the spaces $V'$ and $H$. We apply the results to non-autonomous Robin-boundary conditions and also use maximal regularity to solve a quasilinear problem.< Leer menos

Palabras clave en inglés

wave equation

Sesquilinear forms

non-autonomous evolution equations

maximal regularity

non-linear heat equations

wave equation.

URI

https://oskar-bordeaux.fr/handle/20.500.12278/189544

DOI

http://dx.doi.org/10.1007/s00020-013-2109-6

Proyecto ANR

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

Orígen

Importado de Hal

Centros de investigación

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251