Abstract:
A new method is proposed for finding asymptotics as t→∞ of the solutions of the Cauchy problem for nonlinear evolution equations with nonsmall initial data.
Citation:
P. I. Naumkin, I. A. Shishmarev, “Asymptotics as t→∞ of the solutions of nonlinear equations with nonsmall initial perturbations”, Mat. Zametki, 59:6 (1996), 855–864; Math. Notes, 59:6 (1996), 618–624
\Bibitem{NauShi96}
\by P.~I.~Naumkin, I.~A.~Shishmarev
\paper Asymptotics as $t\to\infty$ of the solutions of nonlinear equations with nonsmall initial perturbations
\jour Mat. Zametki
\yr 1996
\vol 59
\issue 6
\pages 855--864
\mathnet{http://mi.mathnet.ru/mzm1784}
\crossref{https://doi.org/10.4213/mzm1784}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1445471}
\zmath{https://zbmath.org/?q=an:0881.35016}
\transl
\jour Math. Notes
\yr 1996
\vol 59
\issue 6
\pages 618--624
\crossref{https://doi.org/10.1007/BF02307211}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1996VM73200026}
Linking options:
https://www.mathnet.ru/eng/mzm1784
https://doi.org/10.4213/mzm1784
https://www.mathnet.ru/eng/mzm/v59/i6/p855
This publication is cited in the following 12 articles:
Blow-up in Nonlinear Sobolev Type Equations, 2011, 621
M. O. Korpusov, A. G. Sveshnikov, “Blow-up of solutions of strongly nonlinear equations of pseudoparabolic type”, J Math Sci, 148:1 (2008), 1
E. I. Kaikina, P. I. Naumkin, I. A. Shishmarev, “On the Cauchy problem for nonlinear dissipative systems”, J Math Sci, 142:3 (2007), 2113
Hayashi, N, “Asymptotics for dissipative nonlinear equations - Preliminary results”, Asymptotics For Dissipative Nonlinear Equations, 1884 (2006), 1
Kaikina, EI, “Landau-Ginzburg-type equations on the half-line in the critical case”, Proceedings of the Royal Society of Edinburgh Section A-Mathematics, 135 (2005), 1241
Kaikina E.I., “Nonlinear Pseudodifferential Equations on a Segment”, Differ. Integral Equ., 18:2 (2005), 195–224
E. I. Kaikina, P. I. Naumkin, I. A. Shishmarev, “Asymptotics of solutions of non-linear dissipative equations”, Izv. Math., 68:3 (2004), 461–492
Kaikina, EI, “Nonlinear nonlocal Whitham equation on a segment”, Nonlinear Analysis-Theory Methods & Applications, 59:1–2 (2004), 55
Kaikina, EI, “On the asymptotic behavior of solutions to nonlinear dissipative systems of equations”, Doklady Mathematics, 68:1 (2003), 49
M. O. Korpusov, “Global solvability of an initial-boundary value problem for a system of semilinear equations”, Comput. Math. Math. Phys., 42:7 (2002), 1000–1011
I. A. Shishmarev, M. Tsutsumi, “Large time asymptotic behaviour of solutions of the complex Landau–Ginzburg equation”, Sb. Math., 190:4 (1999), 569–588
Shishmarev, IA, “Asymptotics in time for nonlinear nonlocal Shrodinger equations with a source”, Journal of the Mathematical Society of Japan, 51:2 (1999), 463