A local existence theorem of the solution of the Cauchy problem for BBGKY chain of equations represented in cumulant expansions in the space E_{ξ}

Myhaylo O. Stashenko; Halyna M. Hubal

Opuscula Math. 24, no. 1 (2004), 161-168

Opuscula Mathematica

A local existence theorem of the solution of the Cauchy problem for BBGKY chain of equations represented in cumulant expansions in the space E_ξ

Abstract. It is proved convergence of solution in cumulant expansions of the initial value problem for BBGKY chain of equations of non-symmetrical one-dimensional system of particles which interact via a short-range potential in the space \(E_{\xi}\) of the sequences of continuous bounded functions.

Keywords: non-symmetrical particle systems, space of the sequences of continuous bounded functions, BBGKY chain of equations, cumulant.

Mathematics Subject Classification: 35Q30.

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About the authors

Myhaylo O. Stashenko
Volyn State University named after Lesya Ukrainka, Department of Mathematics, 13 Voli av., Lutsk 43025, Ukraine

Halyna M. Hubal
Volyn State University named after Lesya Ukrainka, Department of Mathematics, 13 Voli av., Lutsk 43025, Ukraine

About the article

Received: 2004-05-27.

A local existence theorem of the solution of the Cauchy problem for BBGKY chain of equations represented in cumulant expansions in the space Eξ

A local existence theorem of the solution of the Cauchy problem for BBGKY chain of equations represented in cumulant expansions in the space E_ξ