RESOLVENT ESTIMATE AND ENERGY DECAY FOR PARTIALLY DAMPED HYPERBOLIC SYSTEMS IN EXTERIOR DOMAIN

RESOLVENT ESTIMATE AND ENERGY DECAY FOR PARTIALLY DAMPED HYPERBOLIC SYSTEMS IN EXTERIOR DOMAIN | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 28 August 2025 V1 Latest version Share on RESOLVENT ESTIMATE AND ENERGY DECAY FOR PARTIALLY DAMPED HYPERBOLIC SYSTEMS IN EXTERIOR DOMAIN Authors : LAloui 0009-0009-5712-2619 [email protected] , AArama , and HAzaza Authors Info & Affiliations https://doi.org/10.22541/au.175635915.57144271/v1 160 views 147 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract — In this paper, we study the resolvent associated with a system of two coupled hyperbolic equations (wave-wave or wave-Klein-Gordon) in exterior domains, where only one equation is directly damped. Under the assumptions that the damping and coupling terms are effective at infinity and satisfy the geometric control condition near the boundary, we prove that the resolvent norm in the energy space E grows as 1 + | λ | − 1, while its norm in L ( ( H 1 ) 2 × ( L 2 ) 2, E ) is of order O ( 1 + | λ | − 1 / 2 ) . These estimates allow us to establish a decay rate of at least 1 /t for the total energy of the system with initial data in ( H 1 ) 2 × ( L 2 ) 2 . Moreover, we improve upon existing results in two key aspects: For the wave-wave system, we obtain the same 1 /t energy decay rate as in previous works, but under less restrictive assumptions. For the wave-Klein-Gordon case, we show that the energy of the second component decays at the rate of 1 / t 2, improving the previously known 1 /t decay. Supplementary Material File (aaa1-13-8-25.pdf) Download 510.28 KB Information & Authors Information Version history V1 Version 1 28 August 2025 Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords —damped wave equation energy decay exterior domain klein-gordon equation observability resolvent stability Authors Affiliations LAloui 0009-0009-5712-2619 [email protected] Universite de Tunis El Manar Faculte des Sciences de Tunis View all articles by this author AArama Universite Larbi Ben M'hidi Oum El-Bouaghi Faculte des Sciences et des Sciences Appliquees View all articles by this author HAzaza Universite de Tunis El Manar Faculte des Sciences de Tunis View all articles by this author Metrics & Citations Metrics Article Usage 160 views 147 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation LAloui, AArama, HAzaza. RESOLVENT ESTIMATE AND ENERGY DECAY FOR PARTIALLY DAMPED HYPERBOLIC SYSTEMS IN EXTERIOR DOMAIN. Authorea . 28 August 2025. DOI: https://doi.org/10.22541/au.175635915.57144271/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. 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