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.

Full text (pdf)

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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.
• Accepted: 2016-12-27.
• Published online: 2017-07-05.