Global solutions for a nonlinear absorption parabolic problem in exterior domains

We prove the existence of positive continuous solutions with a precise global behavior for the following nonlinear absorption parabolic equation Δu−uφ(.,u)−∂u∂t=0 in D×(0,∞)D×(0,∞) with boundary conditions u=0u=0 on ∂D×(0,∞)∂D×(0,∞) and u(x,0)=u0(x)u(x,0)=u0(x), where DD is an exterior domain of RnRn, (n≥3)(n≥3). The nonlinear term is required to satisfy some conditions related to the parabolic Kato class introduced in L. Mâatoug and L. Riahi (2006) [5] and the initial data u0u0 may be unbounded. Our approach is based on some potential theory arguments.