Bounded solutions to a singular parabolic system

In this paper, we are concerned with the singular parabolic system ut=Δu+f(x)v−p,vt=Δv+g(x)u−q in a smooth bounded domain Ω⊂RN subject to zero Dirichlet conditions, with initial conditions u0(x),v0(x)>0. This problem is of interest as it is related to some problems in biology and physics. Under suitable assumptions on p,q and f(x),g(x), some existence results of weak and classical solutions are obtained using a functional method. This method is motivated by such results found in [4] and [5] when dealing with singular parabolic systems and the related references within.