{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,19]],"date-time":"2026-01-19T16:19:40Z","timestamp":1768839580916,"version":"3.49.0"},"reference-count":23,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2012,11,29]],"date-time":"2012-11-29T00:00:00Z","timestamp":1354147200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/2.zoppoz.workers.dev:443\/http\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2013,9]]},"DOI":"10.1007\/s11075-012-9658-7","type":"journal-article","created":{"date-parts":[[2012,11,29]],"date-time":"2012-11-29T15:05:54Z","timestamp":1354201554000},"page":"127-155","source":"Crossref","is-referenced-by-count":9,"title":["Finite element approximations of a nonlinear diffusion model with memory"],"prefix":"10.1007","volume":"64","author":[{"given":"Temur","family":"Jangveladze","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zurab","family":"Kiguradze","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Beny","family":"Neta","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Simeon","family":"Reich","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2012,11,29]]},"reference":[{"key":"9658_CR1","unstructured":"Landau, L., Lifschitz, E.: Electrodynamics of Continuous Media. Course of Theoretical Physics, Vol. 8. Pergamon Press, Oxford-London-New York-Paris; Addison-Wesley Publishing Co., Inc., Reading, Mass, 1960, Russian original: Gosudarstv. Izdat. Tehn-Teor. Lit., Moscow (1957, translated from the Russian)"},{"key":"9658_CR2","first-page":"887","volume":"19","author":"D Gordeziani","year":"1983","unstructured":"Gordeziani, D., Dzhangveladze, T., Korshia, T.: Existence and uniqueness of the solution of a class of nonlinear parabolic problems. Differ. Uravn. 19, 1197\u20131207 (1983, Russian). Diff. Equ. 19, 887\u2013895 (1983, English translation)","journal-title":"Diff. Equ."},{"key":"9658_CR3","first-page":"323","volume":"28","author":"TA Dzhangveladze","year":"1983","unstructured":"Dzhangveladze, T.A.: First boundary value problem for a nonlinear equation of parabolic type. Dokl. Akad. Nauk SSSR 269, 839\u2013842 (1983, Russian). Sov. Phys. Dokl. 28, 323\u2013324 (1983, English translation)","journal-title":"Sov. Phys. Dokl."},{"key":"9658_CR4","unstructured":"Dzhangveladze, T.: An Investigation of the First Boundary Value Problem for Some Nonlinear Integro-differential Equations of Parabolic Type. Tbilisi State University, (Russian) (1983)"},{"key":"9658_CR5","first-page":"32","volume":"21","author":"TA Dzhangveladze","year":"1985","unstructured":"Dzhangveladze, T.A.: A nonlinear integro-differential equation of parabolic type. Differ. Uravn. 21, 41\u201346 (1985, Russian). Diff. Equ. 21, 32\u201336 (1985, English translation)","journal-title":"Diff. Equ."},{"key":"9658_CR6","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1070\/SM1989v064n02ABEH003326","volume":"64","author":"G Laptev","year":"1988","unstructured":"Laptev, G.: Quasilinear parabolic equations which contain in coefficients Volterra\u2019s operator. Math. Sbornik 136, 530\u2013545 (1988, Russian). Sbornik Math. 64, 527\u2013542 (1989, English translation)","journal-title":"Sbornik Math."},{"key":"9658_CR7","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1016\/0022-247X(92)90187-I","volume":"168","author":"Y Lin","year":"1992","unstructured":"Lin, Y., Yin, H.M.: Nonlinear parabolic equations with nonlinear functionals. J. Math. Anal. Appl. 168, 28\u201341 (1992)","journal-title":"J. Math. Anal. Appl."},{"key":"9658_CR8","first-page":"51","volume":"23","author":"T Jangveladze","year":"1997","unstructured":"Jangveladze, T.: On one class of nonlinear integro-differential equations. Semin. I. Vekua Inst. Appl. Math. 23, 51\u201387 (1997)","journal-title":"Semin. I. Vekua Inst. Appl. Math."},{"issue":"101","key":"9658_CR9","first-page":"suppl. 289","volume":"59","author":"M Vishik","year":"1962","unstructured":"Vishik, M.: Solvability of boundary-value problems for quasi-linear parabolic equations of higher orders (Russian). Math. Sb. (N.S.) 59(101), suppl. 289\u2013325 (1962)","journal-title":"Math. Sb. (N.S.)"},{"key":"9658_CR10","volume-title":"Quelques M\u00e9thodes de R\u00e9solution des Probl\u00e8mes aux Limites Non-lin\u00e9aires","author":"J-L Lions","year":"1969","unstructured":"Lions, J.-L.: Quelques M\u00e9thodes de R\u00e9solution des Probl\u00e8mes aux Limites Non-lin\u00e9aires. Dunod, Gauthier-Villars, Paris (1969)"},{"key":"9658_CR11","first-page":"21","volume":"30","author":"Z Kiguradze","year":"2004","unstructured":"Kiguradze, Z.: The asymptotic behavior of the solutions of one nonlinear integro-differential model. Semin. I. Vekua Inst. Appl. Math. Reports 30, 21\u201332 (2004)","journal-title":"Semin. I. Vekua Inst. Appl. Math. Reports"},{"key":"9658_CR12","first-page":"58","volume":"19","author":"ZV Kiguradze","year":"2004","unstructured":"Kiguradze, Z.V.: Asymptotic behavior and numerical solution of the system of nonlinear integro-differential equations. Rep. Enl. Sess. Sem. I. Vekua Inst. Appl. Math. 19, 58\u201361 (2004)","journal-title":"Rep. Enl. Sess. Sem. I. Vekua Inst. Appl. Math."},{"key":"9658_CR13","doi-asserted-by":"crossref","first-page":"867","DOI":"10.1007\/s11202-006-0095-5","volume":"47","author":"TA Jangveladze","year":"2006","unstructured":"Jangveladze, T.A., Kiguradze, Z.V.: Asymptotics of a solution of a nonlinear system of diffusion of a magnetic field into a substance. Sib. Mat. Z. 47, 1058\u20131070 (2006, Russian). Sib. Math. J. 47, 867\u2013878 (2006, English translation)","journal-title":"Sib. Math. J."},{"key":"9658_CR14","doi-asserted-by":"crossref","first-page":"382","DOI":"10.1016\/j.jmaa.2008.10.016","volume":"351","author":"T Jangveladze","year":"2009","unstructured":"Jangveladze, T., Kiguradze, Z., Neta, B.: Large time behavior of solutions to a nonlinear integro-differential system. J. Math. Anal. Appl. 351, 382\u2013391 (2009)","journal-title":"J. Math. Anal. Appl."},{"key":"9658_CR15","doi-asserted-by":"crossref","first-page":"254","DOI":"10.1016\/j.camwa.2009.07.052","volume":"59","author":"T Jangveladze","year":"2010","unstructured":"Jangveladze, T., Kiguradze, Z., Neta, B.: Large time asymptotic and numerical solution of a nonlinear diffusion model with memory. Comput. Math. Appl. 59, 254\u2013273 (2010)","journal-title":"Comput. Math. Appl."},{"key":"9658_CR16","doi-asserted-by":"crossref","first-page":"799","DOI":"10.1016\/j.camwa.2008.09.055","volume":"57","author":"T Jangveladze","year":"2009","unstructured":"Jangveladze, T., Kiguradze, Z., Neta, B.: Large time behavior of solutions and finite difference scheme to a nonlinear integro-differential equation. Comput. Math. Appl. 57, 799\u2013811 (2009)","journal-title":"Comput. Math. Appl."},{"key":"9658_CR17","first-page":"38","volume":"48","author":"T Jangveladze","year":"1998","unstructured":"Jangveladze, T.: Convergence of a difference scheme for a nonlinear integro-differential equation. Proc. I. Vekua Inst. Appl. Math. 48, 38\u201343 (1998)","journal-title":"Proc. I. Vekua Inst. Appl. Math."},{"key":"9658_CR18","first-page":"65","volume":"50\u201351","author":"Z Kiguradze","year":"2000","unstructured":"Kiguradze, Z.: Finite difference scheme for a nonlinear integro-differential system. Proc. I. Vekua Inst. Appl. Math 50\u201351, 65\u201372 (2000\u20132001)","journal-title":"Proc. I. Vekua Inst. Appl. Math"},{"key":"9658_CR19","doi-asserted-by":"crossref","first-page":"615","DOI":"10.1016\/j.amc.2009.05.061","volume":"215","author":"T Jangveladze","year":"2009","unstructured":"Jangveladze, T., Kiguradze, Z., Neta, B.: Finite difference approximation of a nonlinear integro-differential system. Appl. Math. Comput. 215, 615\u2013628 (2009)","journal-title":"Appl. Math. Comput."},{"key":"9658_CR20","doi-asserted-by":"crossref","first-page":"598","DOI":"10.1016\/0022-247X(82)90119-6","volume":"89","author":"B Neta","year":"1982","unstructured":"Neta, B.: Numerical solution of a nonlinear integro-differential equation. J. Math. Anal. Appl. 89, 598\u2013611 (1982)","journal-title":"J. Math. Anal. Appl."},{"key":"9658_CR21","doi-asserted-by":"crossref","first-page":"607","DOI":"10.1016\/0022-247X(85)90266-5","volume":"112","author":"B Neta","year":"1985","unstructured":"Neta, B., Igwe, J.O.: Finite differences versus finite elements for solving nonlinear integro-differential equations. J. Math. Anal. Appl. 112, 607\u2013618 (1985)","journal-title":"J. Math. Anal. Appl."},{"key":"9658_CR22","doi-asserted-by":"crossref","first-page":"6883","DOI":"10.1016\/j.amc.2011.01.053","volume":"217","author":"T Jangveladze","year":"2011","unstructured":"Jangveladze, T., Kiguradze, Z., Neta, B.: Galerkin finite element method for one nonlinear integro-differential model. Appl. Math. Comput. 217, 6883\u20136892 (2011)","journal-title":"Appl. Math. Comput."},{"key":"9658_CR23","volume-title":"An Analysis of the Finite Element Method","author":"G Strang","year":"2008","unstructured":"Strang, G., Fix, G.J.: An Analysis of the Finite Element Method, 2nd edn. Wellesley-Cambridge Press, Wellesley, MA (2008)","edition":"2"}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/2.zoppoz.workers.dev:443\/http\/link.springer.com\/content\/pdf\/10.1007\/s11075-012-9658-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/2.zoppoz.workers.dev:443\/http\/link.springer.com\/article\/10.1007\/s11075-012-9658-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/2.zoppoz.workers.dev:443\/http\/link.springer.com\/content\/pdf\/10.1007\/s11075-012-9658-7","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,1]],"date-time":"2019-06-01T05:08:20Z","timestamp":1559365700000},"score":1,"resource":{"primary":{"URL":"https:\/\/2.zoppoz.workers.dev:443\/http\/link.springer.com\/10.1007\/s11075-012-9658-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,11,29]]},"references-count":23,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2013,9]]}},"alternative-id":["9658"],"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1007\/s11075-012-9658-7","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,11,29]]}}}