{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,8]],"date-time":"2026-02-08T11:22:37Z","timestamp":1770549757880,"version":"3.49.0"},"reference-count":24,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2023,4,1]],"date-time":"2023-04-01T00:00:00Z","timestamp":1680307200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,4,1]],"date-time":"2023-04-01T00:00:00Z","timestamp":1680307200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11971104"],"award-info":[{"award-number":["11971104"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Adv Comput Math"],"published-print":{"date-parts":[[2023,4]]},"DOI":"10.1007\/s10444-023-10023-5","type":"journal-article","created":{"date-parts":[[2023,4,10]],"date-time":"2023-04-10T06:02:38Z","timestamp":1681106558000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["On the determination of the spatial-dependent potential coefficient in a linear pseudoparabolic equation"],"prefix":"10.1007","volume":"49","author":[{"given":"Jun-Liang","family":"Fu","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4279-2117","authenticated-orcid":false,"given":"Jijun","family":"Liu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,4,10]]},"reference":[{"issue":"3","key":"10023_CR1","first-page":"146","volume":"33","author":"AI Prilepko","year":"1992","unstructured":"Prilepko, A.I., Kostin, A.B.: Inverse problems of determining the coefficient in a parabolic equation. I. Sibirsk Mat. Zh. 33(3), 146\u2013155 (1992)","journal-title":"Sibirsk Mat. Zh."},{"issue":"3","key":"10023_CR2","first-page":"372","volume":"46","author":"VL Kamynin","year":"2010","unstructured":"Kamynin, V.L., Kostin, A.B.: Two inverse problems of finding a coefficient in a parabolic equation. Diff. Eqns. 46(3), 372\u2013383 (2010)","journal-title":"Diff. Eqns."},{"key":"10023_CR3","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4899-0030-2","volume-title":"Inverse Problems for Partial Differential Equations, Vol. 127 of Appl. Math. Sci.","author":"V Isakov","year":"1998","unstructured":"Isakov, V.: Inverse Problems for Partial Differential Equations, Vol. 127 of Appl. Math. Sci. Spring, New York (1998)"},{"key":"10023_CR4","volume-title":"Methods for Solving Inverse Problems in Mathematical Physics, Vol. 231 of Monographs and Textbooks in Pure and Applied Mathematics","author":"AI Prilepko","year":"2000","unstructured":"Prilepko, A.I., Orlovsky, D.G., Vasin, I.A.: Methods for Solving Inverse Problems in Mathematical Physics, Vol. 231 of Monographs and Textbooks in Pure and Applied Mathematics. Marcel Dekker Inc., New York (2000)"},{"issue":"1","key":"10023_CR5","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1016\/j.cam.2005.06.003","volume":"193","author":"Q Chen","year":"2006","unstructured":"Chen, Q., Liu, J.: Solving an inverse parabolic problem by optimization from final measurement data. J. Comput. Appl. Math. 193(1), 183\u2013203 (2006)","journal-title":"J. Comput. Appl. Math."},{"key":"10023_CR6","volume-title":"Theory of Fluid Flows Through Natural Rocks","author":"GI Barenblatt","year":"1989","unstructured":"Barenblatt, G.I., Entov, V.M., Ryzhik, V.M.: Theory of Fluid Flows Through Natural Rocks. Kluwer Academic Publishers, Dordrecht (1989)"},{"issue":"10","key":"10023_CR7","doi-asserted-by":"publisher","first-page":"3389","DOI":"10.1029\/93WR01495","volume":"29","author":"SM Hassanizadeh","year":"1993","unstructured":"Hassanizadeh, S.M., Gray, W.G.: Thermodynamic basis of capillary pressure in porous media. Water Resour. Res. 29(10), 3389\u20133405 (1993)","journal-title":"Water Resour. Res."},{"issue":"4","key":"10023_CR8","doi-asserted-by":"publisher","first-page":"381","DOI":"10.1017\/S0956792599004210","volume":"11","author":"C Cuesta","year":"2000","unstructured":"Cuesta, C., Duijn, C.V., Hulshof, J.: Infiltration in porous media with dynamic capillary pressure: Travelling waves. Eur. J. Appl. Math. 11 (4), 381\u2013398 (2000)","journal-title":"Eur. J. Appl. Math."},{"issue":"4","key":"10023_CR9","doi-asserted-by":"publisher","first-page":"614","DOI":"10.1007\/BF01594969","volume":"19","author":"PJ Chen","year":"1968","unstructured":"Chen, P.J., Gurtin, M.E.: On a theory of heat conduction involving two temperatures. Z. Angew. Math. Phys. 19(4), 614\u2013627 (1968)","journal-title":"Z. Angew. Math. Phys."},{"issue":"1","key":"10023_CR10","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/BF00250690","volume":"14","author":"TW Ting","year":"1963","unstructured":"Ting, T.W.: Certain non-steady flows of second-order fluids. Arch. Ration. Mech. Anal. 14(1), 1\u201326 (1963)","journal-title":"Arch. Ration. Mech. Anal."},{"issue":"6","key":"10023_CR11","doi-asserted-by":"publisher","first-page":"1414","DOI":"10.1137\/0524082","volume":"24","author":"GI Barenblatt","year":"1993","unstructured":"Barenblatt, G.I., Bertsch, M., Passo, R.D., Ughi, M.: A degenerate pseudoparabolic regularization of a nonlinear forward-backward heat equation arising in the theory of heat and mass exchange in stably stratified turbulent shear flow. SIAM J. Math. Anal. 24(6), 1414\u20131439 (1993)","journal-title":"SIAM J. Math. Anal."},{"issue":"1","key":"10023_CR12","doi-asserted-by":"publisher","first-page":"331","DOI":"10.1090\/S0002-9947-1991-1015926-7","volume":"324","author":"A Novick-Cohen","year":"1991","unstructured":"Novick-Cohen, A., Pego, R.L.: Stable patterns in a viscous diffusion equation. Trans. Amer. Math. Soc. 324(1), 331\u2013351 (1991)","journal-title":"Trans. Amer. Math. Soc."},{"issue":"1","key":"10023_CR13","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1137\/0501001","volume":"1","author":"RE Showalter","year":"1970","unstructured":"Showalter, R.E., Ting, T.W.: Pseudoparabolic partial differential equations. SIAM J. Math. Anal. 1(1), 1\u201326 (1970)","journal-title":"SIAM J. Math. Anal."},{"issue":"6","key":"10023_CR14","doi-asserted-by":"publisher","first-page":"912","DOI":"10.1093\/imamat\/hxm053","volume":"72","author":"M Ptashnyk","year":"2007","unstructured":"Ptashnyk, M.: Pseudoparabolic equations with convection. IMA J. Appl. Math. 72(6), 912\u2013922 (2007)","journal-title":"IMA J. Appl. Math."},{"issue":"1","key":"10023_CR15","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1016\/j.amc.2014.07.095","volume":"246","author":"S Amirov","year":"2014","unstructured":"Amirov, S.: On solvability of the first initial-boundary value problem for quasilinear pseudoparabolic equations. Appl. Math. Comput. 246(1), 112\u2013120 (2014)","journal-title":"Appl. Math. Comput."},{"issue":"3","key":"10023_CR16","doi-asserted-by":"publisher","first-page":"231","DOI":"10.1080\/00036818008839304","volume":"10","author":"W Rundell","year":"1980","unstructured":"Rundell, W., Colton, D.L.: Determination of an unknown nonhomogeneous term in a linear partial differential equation from overspecified boundary data. Appl. Anal. 10(3), 231\u2013242 (1980)","journal-title":"Appl. Anal."},{"key":"10023_CR17","unstructured":"Mamayusupov, M.S.: The problem of determining coefficients of a pseudoparabolic equation. In: Studies in Integro-differential Equations, vol. 16, pp 290\u2013297. Ilim, Frunze (1983)"},{"issue":"2","key":"10023_CR18","first-page":"105","volume":"8","author":"SG Pyatkov","year":"2015","unstructured":"Pyatkov, S.G., Shergin, S.N.: On some mathematical models of filtration type. Bulletin of the South Ural State University Series-Mathematical Modelling Programming and Computer Software 8(2), 105\u2013116 (2015)","journal-title":"Bulletin of the South Ural State University Series-Mathematical Modelling Programming and Computer Software"},{"issue":"10","key":"10023_CR19","doi-asserted-by":"publisher","first-page":"1557","DOI":"10.1080\/00036811.2010.530258","volume":"90","author":"AS Lyubanova","year":"2011","unstructured":"Lyubanova, A.S., Tani, A.: An inverse problem for pseudoparabolic equation of filtration: the existence, uniqueness and regularity. Appl. Anal. 90 (10), 1557\u20131571 (2011)","journal-title":"Appl. Anal."},{"issue":"11","key":"10023_CR20","doi-asserted-by":"publisher","first-page":"1997","DOI":"10.1080\/00036811.2018.1442001","volume":"98","author":"AS Lyubanova","year":"2019","unstructured":"Lyubanova, A.S., Velisevich, A.V.: Inverse problems for the stationary and pseudoparabolic equations of diffusion. Appl. Anal. 98(11), 1997\u20132010 (2019)","journal-title":"Appl. Anal."},{"key":"10023_CR21","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1016\/j.apnum.2022.09.014","volume":"184","author":"J-L Fu","year":"2023","unstructured":"Fu, J.-L., Liu, J.: Recovery of a potential coefficient in a pseudoparabolic system from nonlocal observation. Appl. Numer. Math. 184, 121\u2013136 (2023)","journal-title":"Appl. Numer. Math."},{"issue":"4","key":"10023_CR22","doi-asserted-by":"publisher","first-page":"637","DOI":"10.1090\/S0002-9939-1987-0877031-4","volume":"99","author":"W Rundell","year":"1987","unstructured":"Rundell, W.: The determination of a parabolic equation from initial and final data. Proc. Amer. Math. Soc. 99(4), 637\u2013642 (1987)","journal-title":"Proc. Amer. Math. Soc."},{"issue":"3","key":"10023_CR23","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1088\/0266-5611\/12\/3\/002","volume":"12","author":"M Choulli","year":"1996","unstructured":"Choulli, M., Yamamoto, M.: Generic well-posedness of an inverse parabolic problem\u2013the H\u00f6lder-space approach. Inverse Prob. 12(3), 195\u2013205 (1996)","journal-title":"Inverse Prob."},{"key":"10023_CR24","doi-asserted-by":"publisher","DOI":"10.1515\/9783110208276","volume-title":"Iterative Regularization Methods for Nonlinear Ill-Posed Problems","author":"B Kaltenbacher","year":"2008","unstructured":"Kaltenbacher, B., Neubauer, A., Scherzer, O.: Iterative Regularization Methods for Nonlinear Ill-Posed Problems. Walter de Gruyter, New York (2008)"}],"container-title":["Advances in Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-023-10023-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10444-023-10023-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-023-10023-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,12,10]],"date-time":"2023-12-10T11:49:05Z","timestamp":1702208945000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10444-023-10023-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,4]]},"references-count":24,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2023,4]]}},"alternative-id":["10023"],"URL":"https:\/\/doi.org\/10.1007\/s10444-023-10023-5","relation":{},"ISSN":["1019-7168","1572-9044"],"issn-type":[{"value":"1019-7168","type":"print"},{"value":"1572-9044","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,4]]},"assertion":[{"value":"26 May 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 February 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 April 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"<!--Emphasis Type='Bold' removed-->Competing interests"}}],"article-number":"28"}}