{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,11]],"date-time":"2026-07-11T12:17:47Z","timestamp":1783772267843,"version":"3.55.0"},"reference-count":36,"publisher":"Walter de Gruyter GmbH","issue":"4","funder":[{"DOI":"10.13039\/501100007329","name":"Universidad del Valle","doi-asserted-by":"publisher","award":["1106-712-50006"],"award-info":[{"award-number":["1106-712-50006"]}],"id":[{"id":"10.13039\/501100007329","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007329","name":"Universidad del Valle","doi-asserted-by":"publisher","award":["C. I. 71235"],"award-info":[{"award-number":["C. I. 71235"]}],"id":[{"id":"10.13039\/501100007329","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021,10,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>In this paper, we consider the problem of reconstructing a space-dependent coefficient in a linear Benjamin\u2013Bona\u2013Mahony (BBM)-type equation from a single measurement of its solution at a given time.\nWe analyze the well-posedness of the forward initial-boundary value problem and characterize the inverse problem as a constrained optimization one.\nOur objective consists on reconstructing the variable coefficient in the BBM equation by minimizing an appropriate regularized Tikhonov-type functional constrained by the BBM equation.\nThe well-posedness of the forward problem is studied and approximated numerically by combining a finite-element strategy for spatial discretization using the Python-FEniCS package, together with a second-order implicit scheme for time stepping.\nThe minimization process of the Tikhonov-regularization adopted is performed by using an iterative L-BFGS-B quasi-Newton algorithm as described for instance by Byrd et al. (1995) and Zhu et al. (1997).\nNumerical simulations are presented to demonstrate the robustness of the proposed method with noisy data.\nThe local stability and uniqueness of the solution to the constrained optimization problem for a fixed value of the regularization parameter are also proved and illustrated numerically.<\/jats:p>","DOI":"10.1515\/cmam-2019-0031","type":"journal-article","created":{"date-parts":[[2021,2,28]],"date-time":"2021-02-28T19:27:10Z","timestamp":1614540430000},"page":"873-897","source":"Crossref","is-referenced-by-count":1,"title":["Reconstruction of a Space-Dependent Coefficient in a Linear Benjamin\u2013Bona\u2013Mahony Type Equation"],"prefix":"10.1515","volume":"21","author":[{"given":"Felipe Alexander","family":"Pipicano","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1ticas , Universidad del Valle , Calle 13 Nro 100-00 , Cali , Colombia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6824-1957","authenticated-orcid":false,"given":"Juan Carlos","family":"Mu\u00f1oz Grajales","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas , Universidad del Valle , Calle 13 Nro 100-00 , Cali , Colombia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Anibal","family":"Sosa","sequence":"additional","affiliation":[{"name":"Universidad Icesi , Calle 18 No. 122\u2013135 , Cali , Colombia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"374","published-online":{"date-parts":[[2021,2,25]]},"reference":[{"key":"2026071112041159866_j_cmam-2019-0031_ref_001","doi-asserted-by":"crossref","unstructured":"M. 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