Indirect boundary stabilization of strongly coupled degenerate hyperbolic systems

Indirect boundary stabilization of strongly coupled degenerate hyperbolic systems | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Indirect boundary stabilization of strongly coupled degenerate hyperbolic systems Jawad Salhi, Alhabib Moumni, Mouhcine Tilioua This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3204037/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 15 Feb, 2024 Read the published version in Rendiconti del Circolo Matematico di Palermo Series 2 → Version 1 posted You are reading this latest preprint version Abstract In this paper, we consider the energy decay of a damped hyperbolic system of two degenerate wave equations coupled by velocities when only one equation is directly damped by a linear boundary feedback. To this aim, we first prove that the proposed system is well-posed using the semigroup theory. Then, under the hypothesis that the coupling coefficient is positive and small, we show that the total energy of the whole system decays exponentially. The explicit energy decay rate is established by using the energy multiplier method. MSC 2020: 35B40, 35L80, 93D15, 93D23 Applied Mathematics Coupled degenerate wave equations stabilization exponential decay multiplier techniques Full Text Cite Share Download PDF Status: Published Journal Publication published 15 Feb, 2024 Read the published version in Rendiconti del Circolo Matematico di Palermo Series 2 → Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-3204037","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":221539708,"identity":"d2d699d6-a127-4ceb-9d40-ac1c0881c130","order_by":0,"name":"Jawad Salhi","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAwElEQVRIiWNgGAWjYBACxgYg8bBBQg7KJFZLYoOEMfFawCCxAYSIBcwN7A8/JO6wSN9w7XADw48ahmh+QpoZG3iMJRLPSORuuJ3YwNhzjCF3xgHCWhgkEtsgWhh4GxhyGwhrYX/8A6gl3QBky1+glvmEtTCYgWxJAGlhBtmygaCWZh4zC6AWw5lALYdljknkbiSkxbC9/fGNj2118ny30x8+fFNjkzuPoJZmJA5QsQQB9UAgT1jJKBgFo2AUjHgAAC6wQ2fXXVJjAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0001-9290-9681","institution":"Moulay Ismail University of Meknes","correspondingAuthor":true,"prefix":"","firstName":"Jawad","middleName":"","lastName":"Salhi","suffix":""},{"id":221539783,"identity":"76d6127f-425d-4cb5-a898-5016357047d2","order_by":1,"name":"Alhabib Moumni","email":"","orcid":"","institution":"Moulay Ismail University of Meknes","correspondingAuthor":false,"prefix":"","firstName":"Alhabib","middleName":"","lastName":"Moumni","suffix":""},{"id":221539784,"identity":"7255dcf1-1dbc-4899-8375-060faf1584e0","order_by":2,"name":"Mouhcine Tilioua","email":"","orcid":"","institution":"Moulay Ismail University of Meknes","correspondingAuthor":false,"prefix":"","firstName":"Mouhcine","middleName":"","lastName":"Tilioua","suffix":""}],"badges":[],"createdAt":"2023-07-25 18:59:43","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":true,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false,"coiExplicitlySet":false},"doi":"10.21203/rs.3.rs-3204037/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3204037/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s12215-024-01000-y","type":"published","date":"2024-02-15T13:20:52+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":57352602,"identity":"3beb4a11-5556-4f71-b006-1d5337e4a696","added_by":"auto","created_at":"2024-05-29 13:20:57","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":335995,"visible":true,"origin":"","legend":"","description":"","filename":"salhiindirectboundarystabilizationproblem.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3204037/v1_covered_87d81d2e-b4f4-4dda-9a09-a2cbe798dfff.pdf"}],"financialInterests":"","formattedTitle":"\u003cp\u003eIndirect boundary stabilization of strongly coupled degenerate hyperbolic systems\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"highlight":"","institution":"Universite Moulay Ismail De Meknes","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Coupled degenerate wave equations, stabilization, exponential decay, multiplier techniques","lastPublishedDoi":"10.21203/rs.3.rs-3204037/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3204037/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn this paper, we consider the energy decay of a damped hyperbolic system of two degenerate wave equations coupled by velocities when only one equation is directly damped by a linear boundary feedback. 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