Published January 15, 2023
| Version v1
Publication
A REMARK ON THE LOGARITHMIC DECAY OF THE DAMPED WAVE AND SCHRÖDINGER EQUATIONS ON A COMPACT RIEMANNIAN MANIFOLD
Creators
Contributors
Others:
- Department of Pure Mathematics and Mathematical Statistics (DPMMS) ; Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS) ; University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM)
- Université Nice Sophia Antipolis - Faculté des Sciences (UNS UFR Sciences) ; Université Nice Sophia Antipolis (1965 - 2019) (UNS) ; COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)
- Université Paris-Saclay
- ANR-16-CE40-0013,ISDEEC,Interactions entre Systèmes Dynamiques, Equations d'Evolution et Contrôle(2016)
Description
In this paper we consider a compact Riemannian manifold (M, g) of class C 1 ∩ W 2,∞ and the damped wave or Schrödinger equations on M , under the action of a damping function a = a(x). We establish the following fact: if the measure of the set {x ∈ M ; a(x) = 0} is strictly positive, then the decay in time of the associated energy is at least logarithmic.
Abstract
International audienceAdditional details
Identifiers
- URL
- https://hal.science/hal-03939541
- URN
- urn:oai:HAL:hal-03939541v1
Origin repository
- Origin repository
- UNICA