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

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

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.

Bibliographic Details
Main Authors: Petro Pukach, Volodymyr Il'kiv, Zinovii Nytrebych, Myroslava Vovk
Format: Article
Language:English
Published: AGH Univeristy of Science and Technology Press 2017-01-01
Series:Opuscula Mathematica
Subjects:
boundary value problem
beam vibrations
nonlinear evolution equation
Voigt-Kelvin model
memory
blowup
Online Access:http://www.opuscula.agh.edu.pl/vol37/5/art/opuscula_math_3739.pdf
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spelling doaj-ae0ebf5a12954bba97c9eda503b240b52020-11-24T23:26:23ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742017-01-01375735753http://dx.doi.org/10.7494/OpMath.2017.37.5.7353739On nonexistence of global in time solution for a mixed problem for a nonlinear evolution equation with memory generalizing the Voigt-Kelvin rheological modelPetro Pukach0Volodymyr Il'kiv1Zinovii Nytrebych2Myroslava Vovk3Lviv Polytechnic National University, Department of Mathematics, St. Bandery Str. 12, 79013, Lviv, UkraineLviv Polytechnic National University, Department of Mathematics, St. Bandery Str. 12, 79013, Lviv, UkraineLviv Polytechnic National University, Department of Mathematics, St. Bandery Str. 12, 79013, Lviv, UkraineLviv Polytechnic National University, Department of Mathematics, St. Bandery Str. 12, 79013, Lviv, UkraineThe 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.http://www.opuscula.agh.edu.pl/vol37/5/art/opuscula_math_3739.pdfboundary value problembeam vibrationsnonlinear evolution equationVoigt-Kelvin modelmemoryblowup
collection DOAJ
language English
format Article
sources DOAJ
author Petro Pukach
Volodymyr Il'kiv
Zinovii Nytrebych
Myroslava Vovk
spellingShingle 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 Mathematica
boundary value problem
beam vibrations
nonlinear evolution equation
Voigt-Kelvin model
memory
blowup
author_facet Petro Pukach
Volodymyr Il'kiv
Zinovii Nytrebych
Myroslava Vovk
author_sort Petro Pukach
title On nonexistence of global in time solution for a mixed problem for a nonlinear evolution equation with memory generalizing the Voigt-Kelvin rheological model
title_short On nonexistence of global in time solution for a mixed problem for a nonlinear evolution equation with memory generalizing the Voigt-Kelvin rheological model
title_full On nonexistence of global in time solution for a mixed problem for a nonlinear evolution equation with memory generalizing the Voigt-Kelvin rheological model
title_fullStr On nonexistence of global in time solution for a mixed problem for a nonlinear evolution equation with memory generalizing the Voigt-Kelvin rheological model
title_full_unstemmed On nonexistence of global in time solution for a mixed problem for a nonlinear evolution equation with memory generalizing the Voigt-Kelvin rheological model
title_sort on nonexistence of global in time solution for a mixed problem for a nonlinear evolution equation with memory generalizing the voigt-kelvin rheological model
publisher AGH Univeristy of Science and Technology Press
series Opuscula Mathematica
issn 1232-9274
publishDate 2017-01-01
description 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.
topic boundary value problem
beam vibrations
nonlinear evolution equation
Voigt-Kelvin model
memory
blowup
url http://www.opuscula.agh.edu.pl/vol37/5/art/opuscula_math_3739.pdf
work_keys_str_mv AT petropukach onnonexistenceofglobalintimesolutionforamixedproblemforanonlinearevolutionequationwithmemorygeneralizingthevoigtkelvinrheologicalmodel
AT volodymyrilkiv onnonexistenceofglobalintimesolutionforamixedproblemforanonlinearevolutionequationwithmemorygeneralizingthevoigtkelvinrheologicalmodel
AT zinoviinytrebych onnonexistenceofglobalintimesolutionforamixedproblemforanonlinearevolutionequationwithmemorygeneralizingthevoigtkelvinrheologicalmodel
AT myroslavavovk onnonexistenceofglobalintimesolutionforamixedproblemforanonlinearevolutionequationwithmemorygeneralizingthevoigtkelvinrheologicalmodel
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