a1 Department of Mathematical Physics, The University of Adelaide, Adelaide, 5001, South Australia
Some initial value problems are considered which arise in the treatment of a one-dimensional gas of point particles interacting with a “hard-core” potential.
Two basic types of initial conditions are considered. For the first, one particle is specified to be at the origin with a given velocity. The positions in phase space of the remaining background of particles are represented by continuous distribution functions. The second problem is a periodic analogue of the first.
Exact equations for the delta-function part of the single particle distribution functions are derived for the non-periodic case and approximate equations for the periodic case. These take the form of differential operator equations. The spectral and asymptotic properties of the operators associated with the two cases are examined and compared. The behaviour of the solutions is also considered.
(Received May 31 1978)
p1 Present address: Ames Laboratory, U.S.D.O.E. and Department of Chemistry, Iowa State University, Ames, Iowa, U.S.A. 50011