Abstract:
A model equation is considered, which describes ion acoustic waves in a plasma taking account of strong nonlinear dissipation and nonlinear sources of general form. For the corresponding initial-boundary value
problems in a bounded 3D-domain with zero Dirichlet condition at the boundary of the domain, necessary conditions for the blow-up of a solution are obtained. An estimate for the life time of the solution is also obtained. Finally, it is proved that for any initial data in H10(Ω) the problem under consideration has a local strong generalized solution (in time), that is, it is shown that a blow-up always takes nonzero time.
Bibliography: 16 titles.
Keywords:
finite-time blow-up, nonlinear Sobolev equations, nonlinear mixed boundary value problems, waves in a plasma.
\Bibitem{Kor11}
\by M.~O.~Korpusov
\paper Blow-up of ion acoustic waves in a plasma
\jour Sb. Math.
\yr 2011
\vol 202
\issue 1
\pages 35--60
\mathnet{http://mi.mathnet.ru/eng/sm7670}
\crossref{https://doi.org/10.1070/SM2011v202n01ABEH004137}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2796826}
\zmath{https://zbmath.org/?q=an:1218.35048}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2011SbMat.202...35K}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000290670400003}
\elib{https://elibrary.ru/item.asp?id=19066235}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79955628270}
Linking options:
https://www.mathnet.ru/eng/sm7670
https://doi.org/10.1070/SM2011v202n01ABEH004137
https://www.mathnet.ru/eng/sm/v202/i1/p37
This publication is cited in the following 3 articles:
M. O. Korpusov, “Nonlinear equations of the theory of ion-sound plasma waves”, Comput. Math. Math. Phys., 61:11 (2021), 1886–1894
Dmitry Lukyanenko, Nikolay Nefedov, Lecture Notes in Computer Science, 11386, Finite Difference Methods. Theory and Applications, 2019, 72
M. O. Korpusov, D. V. Lukyanenko, A. A. Panin, E. V. Yushkov, “Blow-up of solutions of a full non-linear equation of ion-sound waves
in a plasma with non-coercive non-linearities”, Izv. Math., 82:2 (2018), 283–317
Citation in format AMSBIB
Contact us: