On the decay of one-dimensional locally and partially dissipated and hyperbolic systems

Crin-Barat T, De Nitti N, Zuazua Iriondo E (2024)

Publication Language: English

Publication Status: Submitted

Publication Type: Unpublished / Preprint

Future Publication Type: Journal article

Publication year: 2024

URI: https://dcn.nat.fau.eu/wp-content/uploads/PartLocDissip-tCrinBarat-nDeNitti-eZuazua.pdf

Open Access Link: https://dcn.nat.fau.eu/wp-content/uploads/PartLocDissip-tCrinBarat-nDeNitti-eZuazua.pdf

Abstract

We study the time-asymptotic behavior of linear hyperbolic systems under partial dissipation which is localized in suitable subsets of the domain. More precisely, we recover the classical decay rates of partially dissipative systems satisfying the stability condition (SK) with a time-delay depending only on the velocity of each component and the size of the undamped region. To quantify this delay, we assume that the undamped region is a bounded space-interval and that the system without spacerestriction on the dissipation satisfies the stability condition (SK). The former assumption ensures that the time spent by the characteristics of the system in the undamped region is finite and the latter that whenever the damping is active the solutions decay. Our approach consists in reformulating the system into n coupled transport equations and showing that the time-decay estimates are delayed by the sum of the times each characteristics spend in the undamped region.

Authors with CRIS profile

Nicola De Nitti Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur) Enrique Zuazua Iriondo Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)

Involved external institutions

University of Deusto / Universidad de Deusto ES Spain (ES)

How to cite

APA:

Crin-Barat, T., De Nitti, N., & Zuazua Iriondo, E. (2024). On the decay of one-dimensional locally and partially dissipated and hyperbolic systems. (Unpublished, Submitted).

MLA:

Crin-Barat, Timothee, Nicola De Nitti, and Enrique Zuazua Iriondo. On the decay of one-dimensional locally and partially dissipated and hyperbolic systems. Unpublished, Submitted. 2024.

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