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Tr. Mat. Inst. Steklova, 2008, Volume 261, Pages 101–114 (Mi tm743)  

This article is cited in 32 scientific papers (total in 32 papers)

Solvability of the Three-Dimensional Thermistor Problem

V. V. Zhikov

Vladimir State Pedagogical University

Abstract: An existence theorem for one of the complicated versions of the well-known thermistor problem is proved.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2008, 261, 98–111

Bibliographic databases:

UDC: 517.956.25
Received in January 2007

Citation: V. V. Zhikov, “Solvability of the Three-Dimensional Thermistor Problem”, Differential equations and dynamical systems, Collected papers, Tr. Mat. Inst. Steklova, 261, MAIK Nauka/Interperiodica, Moscow, 2008, 101–114; Proc. Steklov Inst. Math., 261 (2008), 98–111

Citation in format AMSBIB
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\publ MAIK Nauka/Interperiodica
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. V. Zhikov, S. E. Pastukhova, “Improved integrability of the gradients of solutions of elliptic equations with variable nonlinearity exponent”, Sb. Math., 199:12 (2008), 1751–1782  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. Zhikov V.V., “Solvability of generalized Navier–Stokes equations”, Dokl. Math., 78:3 (2008), 896–900  mathnet  crossref  mathscinet  zmath  isi  elib  elib  scopus
    3. Zhikov V.V., “On passage to the limit in nonlinear elliptic equations”, Dokl. Math., 77:3 (2008), 383–387  mathnet  crossref  mathscinet  zmath  isi  elib  elib  scopus
    4. V. V. Zhikov, “New Approach to the Solvability of Generalized Navier–Stokes Equations”, Funct. Anal. Appl., 43:3 (2009), 190–207  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. Zhikov V.V., Pastukhova S.E., “On the solvability of the Navier–Stokes equations for a compressible b non-Newtonian fluid”, Dokl. Math., 80:1 (2009), 511–515  mathnet  crossref  mathscinet  zmath  isi  elib  elib  scopus
    6. Zhikov V.V., “On the weak convergence of fluxes to a flux”, Dokl. Math., 81:1 (2010), 58–62  crossref  mathscinet  zmath  isi  elib  elib  scopus
    7. Yu. A. Alkhutov, V. V. Zhikov, “Existence theorems for solutions of parabolic equations with variable order of nonlinearity”, Proc. Steklov Inst. Math., 270 (2010), 15–26  mathnet  crossref  mathscinet  zmath  isi  elib
    8. Andreianov B., Bendahmane M., Ouaro S., “Structural stability for variable exponent elliptic problems. II. The $p(u)$-Laplacian and coupled problems”, Nonlinear Anal., 72:12 (2010), 4649–4660  crossref  mathscinet  zmath  isi  elib  scopus
    9. Andreianov B., Bendahmane M., Ouaro S., “Structural stability for variable exponent elliptic problems, I: the $p(x)$-Laplacian kind problems”, Nonlinear Anal., 73:1 (2010), 2–24  crossref  mathscinet  zmath  isi  elib  scopus
    10. V. V. Zhikov, S. E. Pastukhova, “Homogenization of Monotone Operators Under Conditions of Coercitivity and Growth of Variable Order”, Math. Notes, 90:1 (2011), 48–63  mathnet  crossref  crossref  mathscinet  isi
    11. Alkhutov Yu., “Elliptic problems with nonstandard conditions of growth: Zhikov's approach”, Complex Var. Elliptic Equ., 56:7–9 (2011), 559–571  crossref  mathscinet  zmath  isi  elib  scopus
    12. Cherdantsev M., Cherednichenko K.D., “Two-Scale I"-Convergence of Integral Functionals and its Application to Homogenisation of Nonlinear High-Contrast Periodic Composites”, Arch. Ration. Mech. Anal., 204:2 (2012), 445–478  crossref  mathscinet  zmath  isi  elib  scopus
    13. Diening L. Naegele P. Ruzicka M., “Monotone Operator Theory for Unsteady Problems in Variable Exponent Spaces”, Complex Var. Elliptic Equ., 57:11, SI (2012), 1209–1231  crossref  mathscinet  zmath  isi  elib  scopus
    14. Xiang M., Fu Y., “Weak Solutions for Nonlocal Evolution Variational Inequalities Involving Gradient Constraints and Variable Exponent”, Electron. J. Differ. Equ., 2013, 100  mathscinet  isi
    15. Xiang M., “On Nonlinear Evolution Variational Inequalities Involving Variable Exponent”, Electron. J. Qual. Theory Differ., 2013, no. 72, 1–19  crossref  mathscinet  isi
    16. Fu Y., Xiang M., “The Existence of Weak Solutions for Parabolic Variational Inequalities with (P(X,T), Q(X,T))-Growth”, Appl. Anal., 93:1 (2014), 65–83  crossref  mathscinet  zmath  isi  elib  scopus
    17. V. D. Kryakvin, “Boundedness of pseudodifferential operators in Hölder–Zygmund spaces of variable order”, Siberian Math. J., 55:6 (2014), 1073–1083  mathnet  crossref  mathscinet  isi
    18. Bulicek M., Pustejovska P., “Existence Analysis For a Model Describing Flow of An Incompressible Chemically Reacting Non-Newtonian Fluid”, SIAM J. Math. Anal., 46:5 (2014), 3223–3240  crossref  mathscinet  zmath  isi  elib  scopus
    19. Xiang M., “Young Measure Solutions For a Fourth-Order Wave Equation With Variable Growth”, Bound. Value Probl., 2015, 123  crossref  mathscinet  zmath  isi  elib  scopus
    20. Xiang M., Fu Y., Zhang B., “Existence and Boundedness of Solutions For Evolution Variational Inequalities With P(X, T)-Growth”, Electron. J. Differ. Equ., 2015, 172  mathscinet  zmath  isi  elib
    21. Fu Y., Xiang M., “Existence of Solutions For Parabolic Equations of Kirchhoff Type Involving Variable Exponent”, Appl. Anal., 95:3 (2016), 524–544  crossref  mathscinet  zmath  isi  elib  scopus
    22. Byun S.-S., Ok J., “Nonlinear Parabolic Equations with Variable Exponent Growth in Nonsmooth Domains”, SIAM J. Math. Anal., 48:5 (2016), 3148–3190  crossref  mathscinet  zmath  isi  elib  scopus
    23. Byun S.-S., Ok J., “Optimal Gradient Estimates for Parabolic Equations in Variable Exponent Spaces”, Int. Math. Res. Notices, 2016, no. 8, 2493–2521  crossref  mathscinet  isi  elib  scopus
    24. Niu R., Zheng H., Zhang B., “Navier–Stokes Equations in the Half-Space in Variable Exponent Spaces of Clifford-Valued Functions”, Electron. J. Differ. Equ., 2017, 98  mathscinet  zmath  isi
    25. The Anh Bui, Xuan Thinh Duong, “Weighted Lorentz Estimates For Parabolic Equations With Non-Standard Growth on Rough Domains”, Calc. Var. Partial Differ. Equ., 56:6 (2017), 177  crossref  mathscinet  zmath  isi  scopus
    26. Antontsev S.N., Shmarev S.I., “The Energy Method. Application to PDEs of Hydrodynamics With Nonstandard Growth”: A. Chesnokov, E. Pruuel, V. Shelukhin, All-Russian Conference With International Participation Modern Problems of Continuum Mechanics and Explosion Physics Dedicated to the 60th Anniversary of Lavrentyev Institute of Hydrodynamics SB RAS, Journal of Physics Conference Series, 894, IOP Publishing Ltd, 2017, UNSP 012001  crossref  isi  scopus
    27. Byun S.-S., Lee M., Ok J., “Nondivergence Parabolic Equations in Weighted Variable Exponent Spaces”, Trans. Am. Math. Soc., 370:4 (2018), 2263–2298  crossref  mathscinet  zmath  isi  scopus
    28. Avci M., Pankov A., “Multivalued Elliptic Operators With Nonstandard Growth”, Adv. Nonlinear Anal., 7:1 (2018), 35–48  crossref  mathscinet  zmath  isi  scopus
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    30. M. D. Surnachev, “O neravenstve Kharnaka dlya $p(x)$-laplasiana”, Preprinty IPM im. M. V. Keldysha, 2018, 069, 32 pp.  mathnet  crossref
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    32. Yu. A. Alkhutov, M. D. Surnachev, “Povedenie v granichnoi tochke reshenii zadachi Dirikhle dlya $p(x)$-laplasiana”, Algebra i analiz, 31:2 (2019), 88–117  mathnet
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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