Abstract
We prove the existence of positive continuous solutions with a precise global behavior for the following nonlinear absorption parabolic equation Delta u - u phi(., u) - partial derivative u/partial derivative t = 0 in D x (0, infinity) with boundary conditions u = 0 on partial derivative D x (0, infinity) and u(x, 0) = u(0)(x), where D is an exterior domain of R-n, (n >= 3). The nonlinear term is required to satisfy some conditions related to the parabolic Kato class introduced in L. Maatoug and L. Riahi (2006) [5] and the initial data u(0) may be unbounded. Our approach is based on some potential theory arguments. Crown Copyright (C) 2009 Published by Elsevier Ltd. All rights reserved.