FORMATION OF SINGULARITIES IN COMPRESSIBLE EULER-POISSON FLUIDS WITH HEAT DIFFUSION AND DAMPING RELAXATION

We are concerned with a coupling effect of heat diffusion, damping rel axation, and electric potential on the large-time behavior of solution s of the compressible Euler-Poisson fluids starting with smooth initia l data. In this paper we prove that, for smooth initial data with larg e C-1 norm, the corresponding solution will develop singularities in f inite time. This fact indicates that this coupling effect is not stron g enough to prevent the formation of singularities and the development of shock waves in compressible Euler-Poisson fluids as time evolves. (C) 1998 Academic Press.