Decay of the solutions of the generalized Korteweg–de Vries equation at large times
Vestnik rossijskih universitetov. Matematika, Tome 24 (2019) no. 125, pp. 99-111 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper the existence of weak solutions of the nonlinear generalized KdV equation is shown and conditions for which weak solutions decay to zero at large times are obtained.
Keywords: Korteweg–de Vries equation; initial-boundary problem; weak solution; decay.
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A. A. Nikolayev. Decay of the solutions of the generalized Korteweg–de Vries equation at large times. Vestnik rossijskih universitetov. Matematika, Tome 24 (2019) no. 125, pp. 99-111. http://geodesic.mathdoc.fr/item/VTAMU_2019_24_125_a8/

[1] L. Rosier, B.-Y. Zhang, “Global stabilization of the generalized Korteweg–de Vries qquation posed on a finite domain”, SIAM J. Control and Optimization, 45:3 (2006), 927–956 | DOI | MR | Zbl

[2] G. Perla Menzala, C. F. Vasconcellos, E. Zuazua, “Stabilization of the Korteweg–de Vries equation with localized damping”, Quarterly of Applied Mathematics, 60:1 (2002), 111–129 | DOI | MR | Zbl

[3] F. Linares, A. F. Pazoto, “On the exponential decay of the critical generalized Korteweg–de Vries equation with localized damping”, Proceedings of the American Mathematical Society, 135:5 (2007), 1515–1522 | DOI | MR | Zbl

[4] A. V. Faminskii, N. A. Larkin, “Odd-order quasilinear evolution equations posed on a bounded interval”, Bol. Soc. Paranaense Mat., 28:1 (2010), 67–77 | MR | Zbl

[5] A. V. Faminskii, A. Nikolayev, “On stationary solutions of KdV and mKdV equations”, Differential and Difference Equations with Applications, 164 (2016), 63–70 | DOI | MR | Zbl

[6] A. V. Faminskii, “Weak solutions to initial-boundary-value problems for quasilinear evolution equations of an odd order”, Advances in Differential Equations, 17:5-6 (2012), 421–470 | MR | Zbl

[7] A. Pazy, Semigroups of linear operators and applications to partial differential equations, Applied Mathematical Sciences, 44, Springer-Verlag, New York–Heidelberg–Tokyo, 1983 | DOI | MR | Zbl

[8] Y. Kametaka, H. Yamagishi, K. Watanabe, A. Nagai, K. Takemura, “The best constant of Sobolev inequality corresponding to Dirichlet boundary value problem for $(-1)^M (d/dx)^{2M}$”, Sciential Mathematical Japanical Online, 2008, 439–451 | MR