Sticky particles on the line under harmonic interactions

Abstract

We consider the hydrodynamical limit of a system of particles of finite size on the line which interact with each other via an harmonic force. The particles are assumed to stick to each other upon collision, to form compound particles whose mass and size is the sum of masses and sizes of the particles before collision, and whose velocity after collision is determined by the conservation of linear momentum at the collision time. The main result reads: under reasonable conditions on the initial data there exists a unique hydrodynamical limit, and this limit is a weak solution of an associated system of gas dynamics equations.