Bounded solutions to a singular parabolic system

Abstract

In this paper, we are concerned with the singular parabolic system u(t) = Delta u + f (x)v(-p),v(t) = Delta v + g(x)u(-q) in a smooth bounded domain Omega subset of R-N subject to zero Dirichlet conditions, with initial conditions u(0)(x), v(0)(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. (C) 2017 Elsevier Inc. All rights reserved.