LARGE TIME BEHAVIOR FOR THE HEAT-EQUATION WITH ABSORPTION AND CONVECTION

We study the large time behaviour of nonnegative solutions of the Cauc hy problem, u(l) + (u(m)/m)(x) = u(xx) - u(p) in R x R(+) u = u(0) in R x {0}, where 1 < m < 2, p > 1, and u(0) is an element of L(1)(R). We investigate the competition between the diffusion, convection, and ab sorption terms, thus obtaining the asymptotic profile of the solution in L(q)(R) (1 less than or equal to q less than or equal to +infinity) . (C) 1995 Academic Press, Inc.