Geodesic
Wavelet method for solving second-order quasilinear parabolic equations with a conservative principal part
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 9, pp. 1629-1642 Cet article a éte moissonné depuis la source Math-Net.Ru

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A method based on wavelet transforms is proposed for finding classical solutions to initial-boundary value problems for second-order quasilinear parabolic equations. For smooth data, the convergence of the method is proved and the convergence rate of an approximate weak solution to a classical one is estimated in the space of wavelet coefficients. An approximate weak solution of the problem is found by solving a nonlinear system of equations with the help of gradient-type iterative methods with projection onto a fixed subspace of basis wavelet functions. 
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     title = {Wavelet method for solving second-order quasilinear parabolic equations with a~conservative principal part},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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E. M. Abbasov; O. A. Dyshin; B. A. Suleimanov. Wavelet method for solving second-order quasilinear parabolic equations with a conservative principal part. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 9, pp. 1629-1642. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_9_a9/

[1] Ladyzhenskaya O. A., Solonnikov V. A., Uraltseva H. H., Lineinye i kvazilineinye uravneniya parabolicheskogo tipa, Nauka, M., 1967

[2] Ladyzhenskaya O. A., Kraevye zadachi matematicheskoi fiziki, Nauka, M., 1973 | MR

[3] Sobolev S. L., Nekotorye primeneniya funktsionalnogo analiza v matematicheskoi fizike, SO AN SSSR, Novosibirsk, 1962

[4] Karabanova O. V., Kozlov A. I., Kokurin M. Yu., “Ustoichivye konechnomernye iteratsionnye protsessy dlya resheniya nelineinykh nekorrektnykh operatornykh uravnenii”, Zh. vychisl. matem. i matem. fiz., 42:8 (2002), 1115–1128 | MR | Zbl

[5] Bakushinskii A. B., “Iteratsionnye metody gradientnogo tipa s proektirovaniem na fiksirovannoe podprostranstvo dlya resheniya neregulyarnykh operatornykh uravnenii”, Zh. vychisl. matem. i matem. fiz., 40:10 (2000), 1447–1450 | MR

[6] Dobeshi I., Desyat lektsii po veivletam, NITs “Regulyarnaya i khaotich. dinamika”, Moskva–Izhevsk, 2004

[7] Abbasov E. M., Dyshin O. A., Suleimanov B. A., “Primenenie veivlet-preobrazovanii k resheniyu kraevykh zadach dlya lineinykh uravnenii parabolicheskogo tipa”, Zh. vychisl. matem. i matem. fiz., 48:2 (2008), 264–281 | MR | Zbl

[8] Abbasov E. M., Dyshin O. A., Suleimanov B. A., “Veivlet-metod resheniya zadachi nestatsionarnoi filtratsii s razryvnymi koeffitsientami”, Zh. vychisl. matem. i matem. fiz., 48:12 (2008), 2163–2179 | MR

[9] Kudryavtsev L. D., Matematicheskii analiz, T. 1, Vyssh. shkola, M., 1970

[10] Gavurin M. K., Lektsii po metodam vychislenii, Nauka, M., 1971 | MR | Zbl

[11] Novikov I. Ya., Stechkin S. B., “Osnovy teorii vspleskov”, Uspekhi matem. nauk, 53:6 (1998), 53–128 | MR | Zbl

[12] Dremin I. M., Ivanov O. V., Nechitailo V. A., “Veivlety i ikh ispolzovanie”, Uspekhi fiz. nauk, 171:5 (2001), 465–501 | DOI

[13] Deineka B. C., Sergienko I. V., Skopetskii V. V., Modeli i metody resheniya zadach s usloviyami sopryazheniya, Nauk. dumka, Kiev, 1998

[14] Kakhaner D., Mouler K., Nesh S., Chislennye metody i programmnoe obespechenie, Mir, M., 1998

[15] Bakushinskii A. B., Kokurin M. Yu., Yusupova H. A., “Neobkhodimye usloviya skhodimosti iteratsionnykh metodov resheniya nelineinykh operatornykh uravnenii bez svoistva regulyarnosti”, Zh. vychisl. matem. i matem. fiz., 40:7 (2000), 986–996 | MR

[16] Vasilev F. P., Chislennye metody resheniya ekstremalnykh zadach, Nauka, M., 1980 | MR

[17] Starostenko V. I., Ustoichivye chislennye metody v zadachakh gravimetrii, Nauk. dumka, Kiev, 1978 | MR | Zbl

[18] Suleimanov B. A., Abbasov E. M., Efendieva A. O., “Vibrovolnovoe vozdeistvie na plast i prizaboinuyu zonu skvazhin s uchetom effekta proskalzyvaniya”, Inzh.-fiz. zhurnal, 81:2 (2008), 358–364 | MR