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Mat. Zametki, 1999, Volume 65, Issue 1, Pages 70–75 (Mi mz1029)  

This article is cited in 40 scientific papers (total in 40 papers)

An initial-boundary value problem for equations of the generalized Boussinesq equation type with a nonlinear source

A. I. Kozhanov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

DOI: https://doi.org/10.4213/mzm1029

Full text: PDF file (166 kB)
References: PDF file   HTML file

English version:
Mathematical Notes, 1999, 65:1, 59–63

Bibliographic databases:

UDC: 517.946
Received: 17.09.1997

Citation: A. I. Kozhanov, “An initial-boundary value problem for equations of the generalized Boussinesq equation type with a nonlinear source”, Mat. Zametki, 65:1 (1999), 70–75; Math. Notes, 65:1 (1999), 59–63

Citation in format AMSBIB
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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. M. O. Korpusov, “Blow-up of a solution of a pseudoparabolic equation with the time derivative of a nonlinear elliptic operator”, Comput. Math. Math. Phys., 42:12 (2002), 1717–1724  mathnet  mathscinet  zmath
    2. M. O. Korpusov, “Global solvability of pseudoparabolic nonlinear equations and blow-up of their solutions”, Comput. Math. Math. Phys., 42:6 (2002), 814–831  mathnet  mathscinet  zmath
    3. M. O. Korpusov, A. G. Sveshnikov, “Energy estimate of the solution to a nonlinear pseudoparabolic equation at $t\to\infty$”, Comput. Math. Math. Phys., 42:8 (2002), 1154–1160  mathnet  mathscinet  zmath  elib
    4. Korpusov, MO, “Finite-time blow-up of the solution of the Cauchy problem for the pseudoparabolic equation Au-t=F(u)”, Differential Equations, 39:1 (2003), 83  mathnet  crossref  mathscinet  zmath  isi  scopus  scopus
    5. 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
    6. M. O. Korpusov, “Conditions for the global solvability of the Cauchy problem for a semilinear equation of pseudoparabolic type”, Comput. Math. Math. Phys., 43:8 (2003), 1159–1171  mathnet  mathscinet  zmath
    7. 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
    8. M. O. Korpusov, A. G. Sveshnikov, “On the existence of a solution to the Laplace equation with a nonlinear dynamic boundary condition”, Comput. Math. Math. Phys., 43:1 (2003), 92–107  mathnet  mathscinet  zmath
    9. M. O. Korpusov, “Blow-up of solutions of a class of strongly non-linear equations of Sobolev type”, Izv. Math., 68:4 (2004), 783–832  mathnet  crossref  crossref  mathscinet  zmath  isi
    10. M. O. Korpusov, A. G. Sveshnikov, “On the blow-up of the solution of an initial-boundary value problem for a nonlinear nonlocal equation of pseudo-parabolic type”, Comput. Math. Math. Phys., 44:12 (2004), 2104–2111  mathnet  mathscinet  zmath
    11. M. O. Korpusov, A. G. Sveshnikov, “On blowup of a solution to a Sobolev-type equation with a nonlocal source”, Siberian Math. J., 46:3 (2005), 443–452  mathnet  crossref  mathscinet  zmath  isi  elib
    12. M. V. Falaleev, E. Yu. Grazhdantseva, “Fundamental operator-functions of degenerate differential and difference-differential operators in Banach spaces which have a Noether operator in the principal part”, Siberian Math. J., 46:6 (2005), 1123–1134  mathnet  crossref  mathscinet  zmath  isi  elib
    13. E. I. Kaikina, P. I. Naumkin, I. A. Shishmarev, “The Cauchy problem for an equation of Sobolev type with power non-linearity”, Izv. Math., 69:1 (2005), 59–111  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    14. M. O. Korpusov, A. G. Sveshnikov, “Blow-up of solutions of a class of strongly non-linear dissipative wave equations of Sobolev type with sources”, Izv. Math., 69:4 (2005), 733–770  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    15. Korpusov, MO, “Global solvability conditions for an initial-boundary value problem for a nonlinear equation of pseudoparabolic type”, Differential Equations, 41:5 (2005), 712  mathnet  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    16. Kaikina, EI, “On the asymptotic behavior of solutions to the Cauchy problem for a nonlinear Sobolev-type equation”, Doklady Mathematics, 71:2 (2005), 269  zmath  isi  elib
    17. Shishmarev, IA, “On a nonlinear Sobolev type equation”, Differential Equations, 41:1 (2005), 146  mathnet  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    18. M. O. Korpusov, A. G. Sveshnikov, “O neobkhodimom i dostatochnom uslovii razrusheniya resheniya smeshannoi kraevoi zadachi dlya odnogo nelineinogo uravneniya sobolevskogo tipa”, Sib. elektron. matem. izv., 2 (2005), 145–155  mathnet  mathscinet  zmath
    19. M. O. Korpusov, A. G. Sveshnikov, “On the finite-time blowup of solutions to initial–boundary value problems for pseudoparabolic equations with pseudo-Laplacian”, Comput. Math. Math. Phys., 45:2 (2005), 261–274  mathnet  mathscinet  zmath  elib  elib
    20. M. O. Korpusov, A. G. Sveshnikov, “On the blowup of solutions to semilinear pseudoparabolic equations with rapidly growing nonlinearities”, Comput. Math. Math. Phys., 45:1 (2005), 138–148  mathnet  mathscinet  zmath
    21. 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
    22. Hayashi, N, “Asymptotics for dissipative nonlinear equations - Preliminary results”, Asymptotics For Dissipative Nonlinear Equations, 1884 (2006), 1  crossref  isi
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    25. E. I. Kaikina, P. I. Naumkin, I. A. Shishmarev, “Large-time asymptotic behaviour of solutions of non-linear Sobolev-type equations”, Russian Math. Surveys, 64:3 (2009), 399–468  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    26. Lin, YZ, “Solving nonlinear pseudoparabolic equations with nonlocal boundary conditions in reproducing kernel space”, Numerical Algorithms, 52:2 (2009), 173  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    27. E. I. Kaikina, P. I. Naumkin, I. A. Shishmarev, “Periodic Boundary Value Problem for Nonlinear Sobolev-Type Equations”, Funct. Anal. Appl., 44:3 (2010), 171–181  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    28. Cao Ya. Yin J. Jin Ch., “A Periodic Problem of a Semilinear Pseudoparabolic Equation”, Abstract Appl. Anal., 2011, 363579  crossref  mathscinet  zmath  isi  elib  scopus
    29. Kavitova T., “Behavior of the Maximal Solution of the Cauchy Problem for Some Nonlinear Pseudoparabolic Equation as Vertical Bar X Vertical Bar -> Infinity”, Electron. J. Differ. Equ., 2012, 141  mathscinet  zmath  isi  elib
    30. G. A. Sviridyuk, S. A. Zagrebina, “Neklassicheskie modeli matematicheskoi fiziki”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 2012, no. 14, 7–18  mathnet
    31. V. E. Fëdorov, P. N. Davydov, “Polulineinye vyrozhdennye evolyutsionnye uravneniya i nelineinye sistemy gidrodinamicheskogo tipa”, Tr. IMM UrO RAN, 19, no. 4, 2013, 267–278  mathnet  mathscinet  elib
    32. A. A. Bykov, A. S. Sharlo, “Nonstationary contrast structures in adjacency of the special point”, Math. Models Comput. Simul., 7:2 (2015), 165–178  mathnet  crossref
    33. A. A. Bykov, N. N. Nefedov, A. S. Sharlo, “Contrast structures for a quasilinear Sobolev-type equation with unbalanced nonlinearity”, Comput. Math. Math. Phys., 54:8 (2014), 1234–1243  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    34. Zhang H., Lu J., Hu Q., “Exponential Growth of Solution of a Strongly Nonlinear Generalized Boussinesq Equation”, Comput. Math. Appl., 68:12, A (2014), 1787–1793  crossref  mathscinet  zmath  isi  scopus  scopus
    35. Amirov Sh., “On Solvability of the First Initial-Boundary Value Problem For Quasilinear Pseudoparabolic Equations”, Appl. Math. Comput., 246 (2014), 112–120  crossref  mathscinet  zmath  isi  scopus  scopus
    36. Li Y. Cao Ya., “Time Periodic Solutions For a Pseudo-Parabolic Type Equation With Weakly Nonlinear Periodic Sources”, Bull. Malays. Math. Sci. Soc., 38:2 (2015), 667–682  crossref  mathscinet  zmath  isi  scopus  scopus
    37. S. G. Pyatkov, S. N. Shergin, “On some mathematical models of filtration theory”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 8:2 (2015), 105–116  mathnet  crossref  elib
    38. M. V. Plekhanova, “Quasilinear equations that are not solved for the higher-order time derivative”, Siberian Math. J., 56:4 (2015), 725–735  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    39. A. A. Bykov, “Chislennoe reshenie nachalno-kraevoi zadachi dlya psevdoparabolicheskogo uravneniya s vnutrennim perekhodnym sloem”, Model. i analiz inform. sistem, 23:3 (2016), 259–282  mathnet  crossref  mathscinet  elib
    40. Bykov A., Panin A., Sharlo A., “Singularly Perturbed Pseudoparabolic Equation”, Math. Meth. Appl. Sci., 40:6 (2017), 1949–1963  crossref  mathscinet  zmath  isi  scopus  scopus
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