{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,31]],"date-time":"2025-03-31T07:23:28Z","timestamp":1743405808092},"reference-count":5,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Model. Simul. Sci. Comput."],"published-print":{"date-parts":[[2010,9]]},"abstract":"<jats:p> We establish a new model for seepage of a liquid to a chink in the cracked deformable layer, an initial value problem of nonlinear fractional differential equation with variable coefficients, then design a numerical scheme of order 2 to solve this initial value problem. This new model theoretically explains the operating thickness H of a layer depending on the values of pressure gradient on the whole chink rather than on one point, which is practiced by a large amount of data. Compared with the Dontsov equation, our fractional model considers more aspects of the whole process. The earlier rejected results can also be considered in the display lines of the fractional model. <\/jats:p>","DOI":"10.1142\/s1793962310000195","type":"journal-article","created":{"date-parts":[[2010,9,21]],"date-time":"2010-09-21T05:27:48Z","timestamp":1285046868000},"page":"333-347","source":"Crossref","is-referenced-by-count":22,"title":["FEATURES OF SEEPAGE OF A LIQUID TO A CHINK IN THE CRACKED DEFORMABLE LAYER"],"prefix":"10.1142","volume":"01","author":[{"given":"T. S.","family":"ALEROEV","sequence":"first","affiliation":[{"name":"The Academy of National Economy under the Government of the Russian Federation, Moscow 119571, Russia"}]},{"given":"H. T.","family":"ALEROEVA","sequence":"additional","affiliation":[{"name":"MTUCI, Moscow Technical University of Communications and Informatics, Moscow 111024, Russia"}]},{"given":"JIANFEI","family":"HUANG","sequence":"additional","affiliation":[{"name":"LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China"},{"name":"Graduate School of the Chinese Academy of Sciences, Beijing 100190, China"}]},{"given":"NINGMING","family":"NIE","sequence":"additional","affiliation":[{"name":"LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China"},{"name":"Graduate School of the Chinese Academy of Sciences, Beijing 100190, China"}]},{"given":"YIFA","family":"TANG","sequence":"additional","affiliation":[{"name":"LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China"}]},{"given":"SIYAN","family":"ZHANG","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, China"}]}],"member":"219","published-online":{"date-parts":[[2012,1,25]]},"reference":[{"key":"rf1","volume-title":"The Theory of a Non-stationary Filtration of a Liquid and Gas","author":"Barenblatt G. I.","year":"1972"},{"key":"rf2","volume-title":"Hydrodynamics of Oil Cracked Layer","author":"Shaimuratov R. V.","year":"1980"},{"key":"rf3","volume-title":"Development, Research and Exploitation of a Multi-layer Chinks","author":"Krivonosov I. V.","year":"1975"},{"key":"rf4","volume-title":"Hydrodynamics of an Oil Layer","author":"Bulygin B. Ya.","year":"1974"},{"key":"rf5","volume-title":"Fractional Differential Equations","author":"Podlubny I.","year":"1999"}],"container-title":["International Journal of Modeling, Simulation, and Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793962310000195","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T18:49:05Z","timestamp":1565117345000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793962310000195"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,9]]},"references-count":5,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2012,1,25]]},"published-print":{"date-parts":[[2010,9]]}},"alternative-id":["10.1142\/S1793962310000195"],"URL":"https:\/\/doi.org\/10.1142\/s1793962310000195","relation":{},"ISSN":["1793-9623","1793-9615"],"issn-type":[{"value":"1793-9623","type":"print"},{"value":"1793-9615","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,9]]}}}