{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T13:10:59Z","timestamp":1772284259396,"version":"3.50.1"},"publisher-location":"Basel","reference-count":22,"publisher":"Birkh\u00e4user Basel","isbn-type":[{"value":"9783034601511","type":"print"},{"value":"9783034601528","type":"electronic"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2009]]},"DOI":"10.1007\/978-3-0346-0152-8_3","type":"book-chapter","created":{"date-parts":[[2010,1,11]],"date-time":"2010-01-11T11:46:33Z","timestamp":1263210393000},"page":"41-55","source":"Crossref","is-referenced-by-count":2,"title":["Superconducting Vortices: Chapman Full Model"],"prefix":"10.1007","author":[{"given":"S. N.","family":"Antontsev","sequence":"first","affiliation":[]},{"given":"N. V.","family":"Chemetov","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"3_CR1","doi-asserted-by":"publisher","first-page":"263","DOI":"10.1137\/060655146","volume":"39","author":"S.N. a. Antontsev","year":"2007","unstructured":"Antontsev S.N. and Chemetov N.V., Flux of superconducting vortices through a domain, SIAM J. Math. Anal., 39 (2007), pp. 263\u2013280.","journal-title":"SIAM J. Math. Anal."},{"key":"3_CR2","series-title":"Pitman Res. Notes in Mathematics Series","first-page":"1","volume-title":"Progress in partial differential equations. Pont-\u00e0-Mousson 1997","author":"S.N. a. Antontsev","year":"1998","unstructured":"Antontsev S.N. and Gagneux G., Petits param\u00e8tres et passages \u00e0 la limite dans les probl\u00e8mes de filtration diphasique, Progress in partial differential equations. Pont-\u00e0-Mousson 1997, Pitman Res. Notes in Mathematics Series, Longman, Harlow, 1 (1998)."},{"key":"3_CR3","series-title":"Lecture Notes, Novosibirsk State University","volume-title":"Mathematical Questions of the Dynamics of Nonhomogeneous Fluids","author":"S.N. a. Antontsev","year":"1973","unstructured":"Antontsev S.N. and Kazhikhov A.V., Mathematical Questions of the Dynamics of Nonhomogeneous Fluids, Novosibirsk State University, Novosibirsk, 1973. Lecture Notes, Novosibirsk State University."},{"key":"3_CR4","unstructured":"Antontsev S.N., Kazhikhov A.V., and Monakhov V.N., Solvability of boundary value problems for some models of inhomogeneous fluids, Partial Differential Equations, Moscow State University, (1978), pp. 30\u201333. Proceedings of the International Conference dedicated to the memory of I.G. Petrovskii, Moscow, 1976."},{"key":"3_CR5","volume-title":"Boundary value problems in mechanics of nonhomogeneous fluids","author":"S.N. Antontsev","year":"1990","unstructured":"-, Boundary value problems in mechanics of nonhomogeneous fluids, North-Holland Publishing Co., Amsterdam, 1990. Translated from the original Russian edition: Nauka, Novosibirsk, (1983)."},{"key":"3_CR6","doi-asserted-by":"crossref","unstructured":"Briggs A., Claisse J., Elliott C.M., and Styles V.M., Computation of Vorticity Evolution for a Cylindrical II-type superconductor subject tomparalel and transverse applied magnetic fields. In the book: Numerical Methods for Viscosity Solutions and Applications (editors: M. Falcone, C. Makridakis), 2001, pp. 234.","DOI":"10.1142\/9789812799807_0002"},{"key":"3_CR7","doi-asserted-by":"crossref","first-page":"312","DOI":"10.1007\/978-3-663-11374-4","volume-title":"Sobolev spaces on domains","author":"V.I. Burenkov","year":"1998","unstructured":"Burenkov V.I., Sobolev spaces on domains. B.G. Teubner, Stuttgart-Leipzig, (1998) 312 ISBN 3-8154-2068-7 (see also on Web-site of Burenkov V.I.)."},{"key":"3_CR8","unstructured":"Elliott C.M. and Styles V.M., Numerical Approximation of vortex density evolution in a superconductor, in the book: Numerical Analysis 1999, edited by D.F. Griffiths, G.A. Watson, CRC Press, (2000)."},{"key":"3_CR9","doi-asserted-by":"publisher","first-page":"555","DOI":"10.1137\/S0036144599371913","volume":"42","author":"S.J. Chapman","year":"2000","unstructured":"Chapman S.J., A hierarchy of models for type-II superconductors, SIAM Rev., 42 (2000), pp. 555\u2013598 (electronic).","journal-title":"SIAM Rev."},{"key":"3_CR10","doi-asserted-by":"publisher","first-page":"1259","DOI":"10.1137\/S0036139994263665","volume":"55","author":"S.J. Chapman","year":"1995","unstructured":"Chapman S.J., A mean-field model of superconducting vortices in three dimensions, SIAM J. Appl. Math., 55 (1995), pp. 1259\u20131274.","journal-title":"SIAM J. Appl. Math."},{"key":"3_CR11","first-page":"23","volume-title":"ICIAM 99 (Edinburgh)","author":"S.J. Chapman","year":"2000","unstructured":"Chapman S.J., Macroscopic models of superconductivity, in ICIAM 99 (Edinburgh), Oxford Univ. Press, Oxford, 2000, pp. 23\u201334."},{"issue":"1","key":"3_CR12","doi-asserted-by":"publisher","first-page":"92","DOI":"10.1016\/j.physd.2007.08.012","volume":"237","author":"N.V. a. Chemetov","year":"2008","unstructured":"Chemetov N.V. and Antontsev S.N., Euler equations with non-homogeneous Navier slip boundary condition, Physica D: Nonlinear Phenomena, 237,1, 92\u2013105, 2008.","journal-title":"Physica D: Nonlinear Phenomena"},{"issue":"3","key":"3_CR13","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/BF01233674","volume":"32","author":"G.-Q. a. Chen","year":"2001","unstructured":"Chen G.-Q. and Frid H., On the theory of divergence-measure fields and its applications. Bol. Soc. Bras. Mat., 32,3, 1\u201333, 2001.","journal-title":"Bol. Soc. Bras. Mat."},{"key":"3_CR14","doi-asserted-by":"publisher","first-page":"511","DOI":"10.1007\/BF01393835","volume":"98","author":"R.J. a. DiPerna","year":"1989","unstructured":"DiPerna R.J. and Lions P.L., Ordinary differential equations, transport theory and Sobolev spaces. Invent. Math. 98, 511\u2013547 (1989).","journal-title":"Invent. Math."},{"key":"3_CR15","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-61798-0","volume-title":"Elliptic partial differential equations of second order.","author":"D. a. Gilbarg","year":"1983","unstructured":"Gilbarg D. and Trudinger N.S., Elliptic partial differential equations of second order. Springer-Verlag, Berlin, 1983."},{"key":"3_CR16","unstructured":"Kazhikhov A.V., Initial-boundary value problems for the Euler equations of an ideal incompressible fluid, Vestnik Moskov. Univ. Ser. I Mat. Mekh., (1991), pp. 13\u201319, 96."},{"key":"3_CR17","first-page":"47","volume":"33","author":"A.V. Kazhikhov","year":"1992","unstructured":"Kazhikhov A.V., An approach to boundary value problems for equations of composite type, Sibirsk. Mat. Zh., 33 (1992), pp. 47\u201353, 229.","journal-title":"Sibirsk. Mat. Zh."},{"key":"3_CR18","doi-asserted-by":"crossref","DOI":"10.1090\/mmono\/023","volume-title":"Linear and Quasilinear Equations of Parabolic type.","author":"O.A. Ladyzhenskaya","year":"1968","unstructured":"Ladyzhenskaya O.A., Solonnikov V.A., and Ural\u2019tseva N.N., Linear and Quasilinear Equations of Parabolic type. American Mathematical Society, Providence RJ (1968)."},{"key":"3_CR19","volume-title":"Linear and Quasilinear Elliptic Equations.","author":"O.A. a. Ladyzhenskaya","year":"1968","unstructured":"Ladyzhenskaya O.A. and Uraltaeva N.N., Linear and Quasilinear Elliptic Equations. Academic Press, New York and London (1968)."},{"key":"3_CR20","volume-title":"Probl\u00e8mes aux limites non Homog\u00e8nes et Applications","author":"J.L. a. Lions","year":"1968","unstructured":"Lions J.L. and Magenes E., Probl\u00e8mes aux limites non Homog\u00e8nes et Applications. Dunod, Paris (1968)."},{"key":"3_CR21","volume-title":"Function Spaces.","author":"A. Kufner","year":"1977","unstructured":"Kufner A., Jonh O. and Fu\u010dik S., Function Spaces. Noordholf Intern. Publishing, Leyden (1977)."},{"key":"3_CR22","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1007\/BF01762360","volume":"146","author":"J. Simon","year":"1987","unstructured":"Simon J., Compact sets in the space L p (0, T; B), Ann. Mat. Pura Appl., IV. Ser., 146, 1987, 65\u201396.","journal-title":"Compact sets in the space Lp(0, T; B), Ann. Mat. Pura Appl."}],"container-title":["New Directions in Mathematical Fluid Mechanics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-0346-0152-8_3.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,12,10]],"date-time":"2020-12-10T15:54:09Z","timestamp":1607615649000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-0346-0152-8_3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009]]},"ISBN":["9783034601511","9783034601528"],"references-count":22,"URL":"https:\/\/doi.org\/10.1007\/978-3-0346-0152-8_3","relation":{},"subject":[],"published":{"date-parts":[[2009]]}}}