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Mat. Zametki, 2002, Volume 71, Issue 2, Pages 292–297 (Mi mz347)  

This article is cited in 26 scientific papers (total in 26 papers)

The Phase Space of an Initial-Boundary Value Problem for the Hoff Equation

G. A. Sviridyuk, V. O. Kazak

Chelyabinsk State University

Abstract: The Hoff equation $(\lambda +\Delta )u_t=-\alpha u-\beta u^3$ describes the H-beam buckling dynamics. We show that the phase space of the Hoff equation is a simple $C^\infty $ Banach manifold modeled on a subspace complementary to the kernel $\ker (\lambda +\Delta )$.

DOI: https://doi.org/10.4213/mzm347

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English version:
Mathematical Notes, 2002, 71:2, 262–266

Bibliographic databases:

UDC: 517.9
Received: 26.01.2000

Citation: G. A. Sviridyuk, V. O. Kazak, “The Phase Space of an Initial-Boundary Value Problem for the Hoff Equation”, Mat. Zametki, 71:2 (2002), 292–297; Math. Notes, 71:2 (2002), 262–266

Citation in format AMSBIB
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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. G. A. Sviridyuk, V. O. Kazak, “The phase space of one generalized model by Oskolkov”, Siberian Math. J., 44:5 (2003), 877–882  mathnet  crossref  mathscinet  zmath  isi
    2. M. O. Korpusov, A. G. Sveshnikov, “Three-dimensional nonlinear evolution equations of pseudoparabolic type in problems of mathematical physics”, Comput. Math. Math. Phys., 43:12 (2003), 1765–1797  mathnet  mathscinet  zmath
    3. M. O. Korpusov, A. G. Sveshnikov, “On the solvability of strongly nonlinear pseudoparabolic equation with double nonlinearity”, Comput. Math. Math. Phys., 43:7 (2003), 944–961  mathnet  mathscinet  zmath  elib
    4. G. A. Sviridyuk, N. A. Manakova, “An optimal control problem for the Hoff equation”, J. Appl. Industr. Math., 1:2 (2007), 247–253  mathnet  crossref  mathscinet  elib
    5. G. A. Sviridyuk, I. K. Trineeva, “A Whitney fold in the phase space of the Hoff equation”, Russian Math. (Iz. VUZ), 49:10 (2005), 49–55  mathnet  mathscinet  elib
    6. Sviridyuk, GA, “On the phase space fold of a nonclassical equation”, Differential Equations, 41:10 (2005), 1476  mathnet  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    7. G. A. Sviridyuk, O. G. Kitaeva, “Invariant manifolds of the Hoff equation”, Math. Notes, 79:3 (2006), 408–412  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    8. M. O. Korpusov, A. G. Sveshnikov, ““Destruction” of the solution of a strongly nonlinear equation of pseudoparabolic type with double nonlinearity”, Math. Notes, 79:6 (2006), 820–840  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    9. Sviridyuk, GA, “Hoff equations on graphs”, Differential Equations, 42:1 (2006), 139  mathnet  crossref  mathscinet  zmath  isi  scopus  scopus
    10. G. A. Sviridyuk, S. A. Zagrebina, P. O. Pivovarova, “Ustoichivost uravnenii Khoffa na grafe”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 1(20) (2010), 6–15  mathnet  crossref
    11. A. A. Bayazitova, “Chislennoe issledovanie protsessov v modelyakh Khoffa”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 2011, no. 7, 4–9  mathnet  zmath  elib
    12. P. O. Pivovarova, “Neustoichivost reshenii uravnenii Khoffa na grafe. Chislennyi eksperiment”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 2011, no. 7, 71–74  mathnet  zmath  elib
    13. “Georgii anatolevich sviridyuk (k shestidesyatiletiyu so dnya rozhdeniya)”, Vestnik Yuzhno-Uralskogo gosudarstvennogo universiteta. Seriya: Matematicheskoe modelirovanie i programmirovanie, 2012, no. 5, 112–120  elib
    14. S. A. Zagrebina, “Mnogotochechnaya nachalno-konechnaya zadacha dlya lineinoi modeli Khoffa”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 2012, no. 11, 4–12  mathnet  zmath  elib
    15. D. E. Shafranov, A. I. Shvedchikova, “Uravnenie Khoffa kak model uprugoi obolochki”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 2012, no. 12, 77–81  mathnet
    16. Fedorov V.E., Davydov P.N., “On Nonlocal Solutions of Semilinear Equations of the Sobolev Type”, Differ. Equ., 49:3 (2013), 326–335  crossref  mathscinet  zmath  isi  elib  elib  scopus
    17. P. O. Moskvicheva, I. N. Semenova, “The Lyapunov stability of the Cauchy–Dirichlet problem for the generalized Hoff equation”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 7:4 (2014), 126–131  mathnet  crossref
    18. N. A. Manakova, “Matematicheskie modeli i optimalnoe upravlenie protsessami filtratsii i deformatsii”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 8:3 (2015), 5–24  mathnet  crossref  elib
    19. F. L. Hasan, “Solvability of initial problems for one class of dynamical equations in quasi-Sobolev spaces”, J. Comp. Eng. Math., 2:3 (2015), 34–42  mathnet  crossref  elib
    20. N. A. Manakova, G. A. Sviridyuk, “Neklassicheskie uravneniya matematicheskoi fiziki. Fazovye prostranstva polulineinykh uravnenii sobolevskogo tipa”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 8:3 (2016), 31–51  mathnet  crossref  elib
    21. E. M. Buryak, T. K. Plyshevskaya, A. B. Samarov, “Elitnoe matematicheskoe obrazovanie na kafedre uravnenii matematicheskoi fiziki fakulteta matematiki, mekhaniki i kompyuternykh tekhnologii instituta estestvennykh i tochnykh nauk FGAOU VO «YuUrGU (NIU)» (Opyt istoriko-statisticheskogo issledovaniya)”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 9:4 (2016), 159–163  mathnet  elib
    22. Buryak E.M., Plyshevskaya T.K., Samarov A.B., “Elite Mathematical Education At the Department of Equations of Mathematical Physics of the Faculty of Mathematics, Mechanics and Computer Technology of the Institute of Natural and Exact Sciences Fgaou Vo “Yuurgu (Niu)” (Experience of Historical-Statistical Research)”, Bull. South Ural State U. Ser.-Math Model Program Comput., 9:4 (2016), 159–163  isi
    23. Moskvicheva P.O., “The Instability of the Solutions of the Generalized Sobolev Type Equation on a Graph”, 2016 2Nd International Conference on Industrial Engineering, Applications and Manufacturing (Icieam), IEEE, 2016  isi
    24. N. A. Manakova, K. V. Vasiuchkova, “Numerical investigation for the start control and final observation problem in model of an I-beam deformation”, J. Comp. Eng. Math., 4:2 (2017), 26–40  mathnet  crossref  mathscinet  elib
    25. M. A. Sagadeeva, A. V. Generalov, “Numerical solution for non-stationary linearized Hoff equation defined on geometrical graph”, J. Comp. Eng. Math., 5:3 (2018), 61–74  mathnet  crossref  mathscinet  elib
    26. I. I. Kolotov, A. A. Panin, “On Nonextendable Solutions and Blow-Ups of Solutions of Pseudoparabolic Equations with Coercive and Constant-Sign Nonlinearities: Analytical and Numerical Study”, Math. Notes, 105:5 (2019), 694–706  mathnet  crossref  crossref  isi  elib
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