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This article is cited in 2 scientific papers (total in 2 papers)
Procedings of the 3nd International Conference "Mathematical Physics and its Applications"
Equations of Mathematical Physics
On problem of nonexistence of dissipative estimate for discrete kinetic equations
E. V. Radkevich M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow, 119899, Russia
(published under the terms of the Creative Commons Attribution 4.0 International License)
Abstract:
The existence of a global solution to the discrete kinetic equations in Sobolev spaces is proved, its decomposition by summability is obtained, the influence of its oscillations generated by the interaction operator is explored. The existence of a submanifold ${\mathcal M}_{diss}$ of initial data $(u^0, v^0, w^0)$ for which the dissipative solution exists is proved. It’s shown that the interaction operator generates the solitons (progressive waves) as the nondissipative part of the solution when the initial data $(u^0, v^0, w^0)$ deviate from the submanifold ${\mathcal M}_{diss}$. The amplitude of solitons is proportional to the distance from $(u^0, v^0, w^0)$ to the submanifold ${\mathcal M}_{diss}$. It follows that the solution can stabilize as $t\to\infty$ only on compact sets of spatial variables.
Keywords:
dissipative estimates, discrete kinetic equations.
Original article submitted 18/X/2012 revision submitted – 25/XII/2012
Citation:
E. V. Radkevich, “On problem of nonexistence of dissipative estimate for discrete kinetic equations”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 1(30) (2013), 106–143
Linking options:
https://www.mathnet.ru/eng/vsgtu1140 https://www.mathnet.ru/eng/vsgtu/v130/p106
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Abstract page: | 409 | Full-text PDF : | 221 | References: | 67 | First page: | 1 |
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