Opuscula Math. 37, no. 5 (2017), 735-753
http://dx.doi.org/10.7494/OpMath.2017.37.5.735

 
Opuscula Mathematica

On nonexistence of global in time solution for a mixed problem for a nonlinear evolution equation with memory generalizing the Voigt-Kelvin rheological model

Petro Pukach
Volodymyr Il'kiv
Zinovii Nytrebych
Myroslava Vovk

Abstract. The paper deals with investigating of the first mixed problem for a fifth-order nonlinear evolutional equation which generalizes well known equation of the vibrations theory. We obtain sufficient conditions of nonexistence of a global solution in time variable.

Keywords: boundary value problem, beam vibrations, nonlinear evolution equation, Voigt-Kelvin model, memory, blowup.

Mathematics Subject Classification: 35G20, 35G31.

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  • Petro Pukach
  • Lviv Polytechnic National University, Department of Mathematics, St. Bandery Str. 12, 79013, Lviv, Ukraine
  • Volodymyr Il'kiv
  • Lviv Polytechnic National University, Department of Mathematics, St. Bandery Str. 12, 79013, Lviv, Ukraine
  • Zinovii Nytrebych
  • Lviv Polytechnic National University, Department of Mathematics, St. Bandery Str. 12, 79013, Lviv, Ukraine
  • Myroslava Vovk
  • Lviv Polytechnic National University, Department of Mathematics, St. Bandery Str. 12, 79013, Lviv, Ukraine
  • Communicated by Vicentiu D. Radulescu.
  • Received: 2016-07-22.
  • Accepted: 2016-12-27.
  • Published online: 2017-07-05.
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Cite this article as:
Petro Pukach, Volodymyr Il'kiv, Zinovii Nytrebych, Myroslava Vovk, On nonexistence of global in time solution for a mixed problem for a nonlinear evolution equation with memory generalizing the Voigt-Kelvin rheological model, Opuscula Math. 37, no. 5 (2017), 735-753, http://dx.doi.org/10.7494/OpMath.2017.37.5.735

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