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TMF, 2012, Volume 171, Number 1, Pages 3–17 (Mi tmf6924)  

This article is cited in 5 scientific papers (total in 5 papers)

Blowup of a positive-energy solution of model wave equations in nonlinear dynamics

M. O. Korpusov

M. V. Lomonosov Moscow State University

Abstract: We consider four problems of model nonlinear equations appearing in nonlinear mechanics and obtain sufficient conditions for the finite-time blowup of the problem solutions in bounded domains with homogeneous Dirichlet conditions. The initial system energy can be an arbitrarily large positive quantity. We use a modified Levin method to prove the blowup.

Keywords: finite-time blowup, generalized Klein–Gordon equation, nonlinear hyperbolic equation, nonlinear mixed boundary value problem, field theory

DOI: https://doi.org/10.4213/tmf6924

Full text: PDF file (443 kB)
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English version:
Theoretical and Mathematical Physics, 2012, 171:1, 421–434

Bibliographic databases:

Received: 18.06.2011

Citation: M. O. Korpusov, “Blowup of a positive-energy solution of model wave equations in nonlinear dynamics”, TMF, 171:1 (2012), 3–17; Theoret. and Math. Phys., 171:1 (2012), 421–434

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. N. Kolkovska, M. Dimova, N. Kutev, “_orig generalized nehari functionals and finite time blow up of the solutions to boussinesq equation”, Recent Developments in Nonlinear Acoustics, 20th International Symposium on Nonlinear Acoustics including the 2nd International Sonic Boom Forum (Ecully, France, 29 June–3 July 2015), AIP Conference Proceedings, 1684, ed. M. Todorov, Amer Inst Physics, 2015, 080008  crossref  isi  scopus
    2. N. Kutev, N. Kolkovska, M. Dimova, “Nonexistence of global solutions to new ordinary differential inequality and applications to nonlineardispersive equations”, Math. Meth. Appl. Sci., 39:9 (2016), 2287–2297  crossref  mathscinet  zmath  isi  elib  scopus
    3. N. Kutev, N. Kolkovska, M. Dimova, “Sign-preserving functionals and blow-up to Klein–Gordon equation with arbitrary high energy”, Appl. Anal., 95:4 (2016), 860–873  crossref  mathscinet  zmath  isi  elib  scopus
    4. J. A. Esquivel-Avila, “Remarks on the qualitative behavior of the undamped Klein–Gordon equation”, Proceedings of Equadiff 2017 Conference, eds. K. Mikula, D. Sevcovic, J. Urban, Spektrum Stu Publishing, 2017, 221–228  mathscinet  isi
    5. J. A. Esquivel-Avila, “Nonexistence of global solutions of abstract wave equations with high energies”, J. Inequal. Appl., 2017, 268  crossref  mathscinet  zmath  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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