On problem of nonexistence of dissipative estimate for discrete kinetic equations

• Main Author: E. V. Radkevich
• Format: Article
• Language: English
• Published: Samara State Technical University 2013-03-01
• Series: Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki
• Online Access: http://mi.mathnet.ru/eng/vsgtu1140

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 Mdiss of initial data (u0,v0,w0) 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 (u0,v0,w0) deviate from the submanifold Mdiss. The amplitude of solitons is proportional to the distance from (u0,v0,w0) to the submanifold Mdiss. It follows that the solution can stabilize as t→∞ only on compact sets of spatial variables.