Mixed boundary value problems for the Vlasov system in the quarter-plane

Gennadii V. Demidenko

0000-0001-6338-7247

Scopus Author ID: 6701652666

1. Sobolev Institute of Mathematics SBRAS, Novosibirsk, Russia

2. Novosibirsk State University, Novosibirsk, Russia

demidenk@math.nsc.ru

The paper considers mixed boundary value problems in a quarter-plane for the Vlasov system describing small bending-torsional vibrations of an elastic rod. A criterion for the satisfaction of the Lopatinskii condition is obtained in terms of coefficients of the boundary operators. The existence and uniqueness of solutions in anisotropic weighted Sobolev spaces \linebreak $W_{2,\gamma}^{2,4}(\mathbb{R}_{++}^2)$ are proved, sharp estimates of solutions in integral norms are obtained, and explicit formulas for the solutions are constructed.

УДК 517.954

Keywords: Vlasov system, pseudohyperbolic systems, mixed boundary value problems, anisotropic weighted Sobolev spaces