Abstract:
We consider the initial-boundary value problem for a dissipative nonlinear wave equation of the Sobolev type with a nonlocal cubic source. For this problem we obtain a sufficient condition for blowup of a strong generalized solution. Moreover, we obtain a two-sided estimate for the blowup time of the solution.
Citation:
M. O. Korpusov, A. G. Sveshnikov, “On blowup of a solution to a Sobolev-type equation with a nonlocal source”, Sibirsk. Mat. Zh., 46:3 (2005), 567–578; Siberian Math. J., 46:3 (2005), 443–452
\Bibitem{KorSve05}
\by M.~O.~Korpusov, A.~G.~Sveshnikov
\paper On blowup of a solution to a Sobolev-type equation with a~nonlocal source
\jour Sibirsk. Mat. Zh.
\yr 2005
\vol 46
\issue 3
\pages 567--578
\mathnet{http://mi.mathnet.ru/smj988}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2164561}
\zmath{https://zbmath.org/?q=an:1094.35066}
\elib{https://elibrary.ru/item.asp?id=13697872}
\transl
\jour Siberian Math. J.
\yr 2005
\vol 46
\issue 3
\pages 443--452
\crossref{https://doi.org/10.1007/s11202-005-0047-5}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000229958200008}
Linking options:
https://www.mathnet.ru/eng/smj988
https://www.mathnet.ru/eng/smj/v46/i3/p567
This publication is cited in the following 6 articles:
Serik Aitzhanov, Kymbat Bekenayeva, Zamira Abdikalikova, “Boundary Value Problem for a Loaded Pseudoparabolic Equation with a Fractional Caputo Operator”, Mathematics, 11:18 (2023), 3987
Stanilslav N. Antontsev, Serik E. Aitzhanov, Dinara T. Zhanuzakova, “An initial boundary value problem for a pseudoparabolic equation with a nonlinear boundary condition”, Math Methods in App Sciences, 46:1 (2023), 1111
Aitzhanov S.E., Berdyshev A.S., Bekenayeva K.S., “Solvability Issues of a Pseudo-Parabolic Fractional Order Equation With a Nonlinear Boundary Condition”, Fractal Fract., 5:4 (2021), 134
Di H., Shang Ya., “Blow Up of Solutions For a Class of Fourth Order Nonlinear Pseudo-Parabolic Equation With a Nonlocal Source”, Bound. Value Probl., 2015, 109
Blow-up in Nonlinear Sobolev Type Equations, 2011, 621
Citation in format AMSBIB
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