Shock waves in young supernova remnants (SNR) are generally considered to be the places where production and acceleration of charged particles (relativistic electrons and cosmic rays) take place. Older remnants can be re-energised if an active pulsar catches up with the shell of the remnant (Shull, Fesen, & Saken 1989). In that case a pulsar-driven wind can inject energetic particles into the shell, resulting into a rejuvenation of the radio emission of the old remnant due to the presence of additional relativistic electrons.

Radio observations of CTB80 (Angerhofer et al. 1981) and G5.4-1.2 (Frail & Kulkarni 1991) give evidence for the importance of the presence of an active pulsar close to the old shell of the remnants. In the first case the pulsar is believed to be inside the SNR. In the second case the pulsar is thought to have penetrated the shell of the SNR, and resides in the interstellar medium (ISM). We intend to investigate the physics which are connected with these kind of systems. One expects new effects resulting from the interaction of the three different shocks; the SNR shock, the bowshock bounding the pulsar wind nebula (PWN) and the (pulsar) wind termination shock. The dynamics of the system is described by a hydrodynamics code. We use the results from the hydrodynamics code to investigate the process of acceleration and transport of particles which are advected by the flow and diffuse with respect to the flow. We have applied the latter to a simple problem, the case of a spherically expanding SNR.