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Tr. Mosk. Mat. Obs., 1961, Volume 10, Pages 297–350 (Mi mmo123)  

This article is cited in 38 scientific papers (total in 38 papers)

Equations of parabolic type in a Banach space

P. E. Sobolevskii

Voronezh

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Received: 12.06.1960

Citation: P. E. Sobolevskii, “Equations of parabolic type in a Banach space”, Tr. Mosk. Mat. Obs., 10, 1961, 297–350

Citation in format AMSBIB
\Bibitem{Sob61}
\by P.~E.~Sobolevskii
\paper Equations of parabolic type in a Banach space
\serial Tr. Mosk. Mat. Obs.
\yr 1961
\vol 10
\pages 297--350
\mathnet{http://mi.mathnet.ru/mmo123}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=141900}
\zmath{https://zbmath.org/?q=an:0141.32701}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. A. Pogorelenko, P. E. Sobolevskii, “Giperbolicheskie uravneniya v banakhovom prostranstve”, UMN, 22:1(133) (1967), 170–172  mathnet  mathscinet
    2. Yu. S. Kolesov, “Study of stability of solutions of second order parabolic equations in the critical case”, Math. USSR-Izv., 3:6 (1969), 1277–1291  mathnet  crossref  mathscinet  zmath
    3. N. A. Krasnoborov, “An investigation of the stability of solutions of a quasilinear operator equation of parabolic type”, Russian Math. Surveys, 34:4 (1979), 170–170  mathnet  crossref  mathscinet  zmath
    4. S. Ya. Yakubov, “A nonlocal boundary value problem for a class of Petrovskii well-posed equations”, Math. USSR-Sb., 46:2 (1983), 255–265  mathnet  crossref  mathscinet  zmath
    5. A. B. Vasil'eva, S. A. Kashchenko, Yu. S. Kolesov, N. Kh. Rozov, “Bifurcation of self-oscillations of nonlinear parabolic equations with small diffusion”, Math. USSR-Sb., 58:2 (1987), 491–503  mathnet  crossref  mathscinet  zmath
    6. A. Yu. Kolesov, “The structure of a neighborhood of a homogeneous cycle in a medium with diffusion”, Math. USSR-Izv., 34:2 (1990), 355–372  mathnet  crossref  mathscinet  zmath
    7. Yu. S. Kolesov, “Attractors of resonance wave type equations: Discontinuous oscillations”, Math. Notes, 56:1 (1994), 679–684  mathnet  crossref  mathscinet  zmath  isi
    8. A. Yu. Kolesov, N. Kh. Rozov, “Characteristic features of the dynamics of the Ginzburg–Landau equation in a plane domain”, Theoret. and Math. Phys., 125:2 (2000), 1476–1488  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    9. Yu. S. Kolesov, “Justification of the method of quasinormal forms for Hutchinson's equation with a small diffusion coefficient”, Izv. Math., 65:4 (2001), 749–768  mathnet  crossref  crossref  mathscinet  zmath
    10. A. Yu. Kolesov, A. N. Kulikov, N. Kh. Rozov, “Attractors of Singularly Perturbed Parabolic Systems of First Degree of Nonroughness in a Plane Domain”, Math. Notes, 75:5 (2004), 617–622  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    11. H. Amann, “Non-local quasi-linear parabolic equations”, Russian Math. Surveys, 60:6 (2005), 1021–1033  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    12. V. B. Levenshtam, “Asymptotic integration of parabolic problems with large high-frequency summands”, Siberian Math. J., 46:4 (2005), 637–651  mathnet  crossref  mathscinet  zmath  isi
    13. A. Yu. Kolesov, E. F. Mishchenko, N. Kh. Rozov, “Buffer Phenomenon in Nonlinear Physics”, Proc. Steklov Inst. Math., 250 (2005), 102–168  mathnet  mathscinet  zmath
    14. V. G. Zvyagin, M. V. Turbin, “The study of initial-boundary value problems for mathematical models of the motion of Kelvin–Voigt fluids”, Journal of Mathematical Sciences, 168:2 (2010), 157–308  mathnet  crossref  mathscinet  elib
    15. M. K. Balaev, “Solvability of the Cauchy Problem for Linear Operator-Differential Equations with Variable Operator Coefficients”, Math. Notes, 90:5 (2011), 651–665  mathnet  crossref  crossref  mathscinet  isi
    16. D. A. Kulikov, A. S. Rudyi, “Formirovanie volnovogo nanorelefa pri raspylenii poverkhnosti ionnoi bombardirovkoi. Nelokalnaya model erozii”, Model. i analiz inform. sistem, 19:5 (2012), 40–49  mathnet
    17. A. V. Glushak, H. K. Avad, “On the solvability of an abstract differential equation of fractional order with a variable operator”, Journal of Mathematical Sciences, 202:5 (2014), 637–652  mathnet  crossref
    18. V. G. Zvyagin, V. P. Orlov, “Weak solvability of a system of thermoviscoelasticity for Jeffris model”, Russian Math. (Iz. VUZ), 57:9 (2013), 53–57  mathnet  crossref
    19. A. M. Kovaleva, D. A. Kulikov, “Odnomodovye i dvukhmodovye neodnorodnye dissipativnye struktury v nelokalnoi modeli erozii”, Model. i analiz inform. sistem, 22:5 (2015), 665–681  mathnet  crossref  mathscinet  elib
    20. A. M. Kovaleva, A. N. Kulikov, D. A. Kulikov, “Ustoichivost i bifurkatsii volnoobraznykh reshenii dlya odnogo funktsionalno-differentsialnogo uravneniya”, Izv. IMI UdGU, 2015, no. 2(46), 60–68  mathnet  elib
    21. A. N. Kulikov, D. A. Kulikov, “Nelokalnaya model formirovaniya relefa pod vozdeistviem potoka ionov. Neodnorodnye nanostruktury”, Matem. modelirovanie, 28:3 (2016), 33–50  mathnet  elib
    22. A. R. Khanalyev, “O koertsitivnoi razreshimosti parabolicheskikh uravnenii s peremennym operatorom”, Trudy Krymskoi osennei matematicheskoi shkoly-simpoziuma, SMFN, 61, RUDN, M., 2016, 164–181  mathnet
    23. L. E. Rossovskii, A. R. Khanalyev, “Koertsitivnaya razreshimost nelokalnykh kraevykh zadach dlya parabolicheskikh uravnenii”, Trudy seminara po differentsialnym i funktsionalno-differentsialnym uravneniyam v RUDN pod rukovodstvom A. L. Skubachevskogo, SMFN, 62, RUDN, M., 2016, 140–151  mathnet
    24. A. N. Kulikov, D. A. Kulikov, “Local bifurcations in the periodic boundary value problem for the generalized Kuramoto–Sivashinsky equation”, Autom. Remote Control, 78:11 (2017), 1955–1966  mathnet  crossref  isi  elib
    25. V. P. Orlov, D. A. Rode, M. A. Pliev, “Weak solvability of the generalized Voigt viscoelasticity model”, Siberian Math. J., 58:5 (2017), 859–874  mathnet  crossref  crossref  isi  elib  elib
    26. A. N. Kulikov, A. V. Sekatskaya, “Lokalnye attraktory v odnoi kraevoi zadache dlya uravneniya Kuramoto—Sivashinskogo”, Materialy mezhdunarodnoi konferentsii «Geometricheskie metody v teorii upravleniya i matematicheskoi fizike: differentsialnye uravneniya, integriruemost, kachestvennaya teoriya» Ryazan, 15–18 sentyabrya 2016 g., Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 148, VINITI RAN, M., 2018, 58–65  mathnet  mathscinet
    27. A. M. Kovaleva, D. A. Kulikov, “Bifurkatsii prostranstvenno neodnorodnykh reshenii v dvukh versiyakh nelokalnogo uravneniya erozii”, Materialy mezhdunarodnoi konferentsii «Geometricheskie metody v teorii upravleniya i matematicheskoi fizike: differentsialnye uravneniya, integriruemost, kachestvennaya teoriya» Ryazan, 15–18 sentyabrya 2016 g., Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 148, VINITI RAN, M., 2018, 66–74  mathnet  mathscinet
    28. A. M. Kovaleva, “Bifurkatsii reshenii odnogo uravneniya s otklonyayuschimsya prostranstvennym argumentom”, Materialy mezhdunarodnoi konferentsii “Geometricheskie metody v teorii upravleniya i matematicheskoi fizike”, posvyaschennoi 70-letiyu S.L. Atanasyana, 70-letiyu I.S. Krasilschika, 70-letiyu A.V. Samokhina, 80-letiyu V.T. Fomenko. Ryazanskii gosudarstvennyi universitet im. S.A. Esenina, Ryazan, 25–28 sentyabrya 2018 g. Chast 1, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 168, VINITI RAN, M., 2019, 33–44  mathnet  crossref
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    30. A. V. Sekatskaya, “Sostoyaniya ravnovesiya vtorogo roda uravneniya Kuramoto—Sivashinskogo s odnorodnymi kraevymi usloviyami Neimana”, Materialy mezhdunarodnoi konferentsii “Geometricheskie metody v teorii upravleniya i matematicheskoi fizike”, posvyaschennoi 70-letiyu S.L. Atanasyana, 70-letiyu I.S. Krasilschika, 70-letiyu A.V. Samokhina, 80-letiyu V.T. Fomenko. Ryazanskii gosudarstvennyi universitet im. S.A. Esenina, Ryazan, 25–28 sentyabrya 2018 g. Chast 1, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 168, VINITI RAN, M., 2019, 80–90  mathnet  crossref
    31. A. S. Zapov, “Ob odnoi matematicheskoi modeli v teorii uprugoi ustoichivosti”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 29:1 (2019), 29–39  mathnet  crossref  elib
    32. V. B. Levenshtam, “Parabolic Equations with Large Parameter. Inverse Problems”, Math. Notes, 107:3 (2020), 452–463  mathnet  crossref  crossref  mathscinet  isi  elib
    33. A. B. Aliev, G. Kh. Shafiyeva, “Mixed Problem with Dynamical Boundary Condition for a One-Dimensional Wave Equation with Strong Dissipation”, Math. Notes, 107:3 (2020), 518–521  mathnet  crossref  crossref  mathscinet  isi  elib
    34. A. N. Kulikov, D. A. Kulikov, “A possibility of realizing the Landau–Hopf scenario in the problem of tube oscillations under the action of a fluid flow”, Theoret. and Math. Phys., 203:1 (2020), 501–511  mathnet  crossref  crossref  mathscinet  isi  elib
    35. A. M. Kovaleva, “Bifurkatsii prostranstvenno neodnorodnykh reshenii v modifitsirovannom variante uravneniya Kuramoto—Sivashinskogo”, Materialy Vserossiiskoi nauchnoi konferentsii «Differentsialnye uravneniya i ikh prilozheniya», posvyaschennoi 85-letiyu professora M. T. Terekhina. Ryazanskii gosudarstvennyi universitet im. S.A. Esenina, Ryazan, 17–18 maya 2019 g. Chast 1, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 185, VINITI RAN, M., 2020, 58–71  mathnet  crossref
    36. A. N. Kulikov, “Inertsialnye invariantnye mnogoobraziya nelineinoi polugruppy operatorov v gilbertovom prostranstve”, Materialy Vserossiiskoi nauchnoi konferentsii «Differentsialnye uravneniya i ikh prilozheniya», posvyaschennoi 85-letiyu professora M. T. Terekhina. Ryazanskii gosudarstvennyi universitet im. S.A. Esenina, Ryazan, 17–18 maya 2019 g. Chast 2, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 186, VINITI RAN, M., 2020, 57–66  mathnet  crossref
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