{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,11]],"date-time":"2026-05-11T11:09:30Z","timestamp":1778497770295,"version":"3.51.4"},"reference-count":59,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2025,7,23]],"date-time":"2025-07-23T00:00:00Z","timestamp":1753228800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"funder":[{"DOI":"10.13039\/501100001665","name":"Agence Nationale de la Recherche","doi-asserted-by":"publisher","award":["ANR-23-CE48-0001-01"],"award-info":[{"award-number":["ANR-23-CE48-0001-01"]}],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,7,23]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>In this paper, we consider the control of a transport equation interconnected with a reaction-diffusion equation, resulting in a transport-reaction-diffusion cascade. The couplings between the different subsystems appear in the two boundary conditions of the reaction-diffusion equation and in the domain. These boundary couplings can be interpreted as pointwise delayed inputs acting on the reaction-diffusion equation, while the in-domain coupling is seen as a spatially varying input delay. This combination of inputs presents significant challenges as applying state-of-the-art approaches\u2014such as backstepping transformations or spectral-reduction techniques\u2014are insufficient for addressing the complexities involved. In this paper, we take advantage of the distinct features of these two methods to develop a new effective feedback control strategy for the studied partial differential equation cascade. Additionally, we provide a necessary and sufficient controllability condition for designing a stabilizing state feedback controller. Notably, we illustrate the existence of specific couplings between the two subsystems of the cascade for which stabilization of the system is not achievable.<\/jats:p>","DOI":"10.1093\/imamci\/dnaf019","type":"journal-article","created":{"date-parts":[[2025,7,24]],"date-time":"2025-07-24T04:26:00Z","timestamp":1753331160000},"source":"Crossref","is-referenced-by-count":0,"title":["Boundary control of transport-reaction-diffusion cascade with simultaneous in-domain and boundary couplings"],"prefix":"10.1093","volume":"42","author":[{"given":"Jean","family":"Auriol","sequence":"first","affiliation":[{"name":"Universit\u00e9 Paris-Saclay , CNRS, CentraleSup\u00e9lec, Laboratoire des signaux et syst\u00e8mes, 91190 Gif-sur-Yvette ,","place":["France"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hugo","family":"Lhachemi","sequence":"additional","affiliation":[{"name":"Universit\u00e9 Paris-Saclay , CNRS, CentraleSup\u00e9lec, Laboratoire des signaux et syst\u00e8mes, 91190 Gif-sur-Yvette ,","place":["France"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2025,7,24]]},"reference":[{"key":"2026051106114832800_ref1","doi-asserted-by":"crossref","first-page":"1095","DOI":"10.1109\/TAC.2012.2228035","article-title":"Disturbance rejection in 2 x 2 linear hyperbolic systems","volume":"58","author":"Aamo","year":"2012","journal-title":"IEEE Trans. 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