ASYMPTOTIC-BEHAVIOR FOR 2 REGULARIZATIONS OF THE CAUCHY-PROBLEM FOR THE BACKWARD HEAT-EQUATION

One method of regularizing the initial value problem for the backward heat equation involves replacing the equation by a singularly perturbe d hyperbolic equation which is equivalent to a damped wave equation wi th negative damping. Another regularization of this problem is obtaine d by perturbing the initial condition rather than the differential equ ation. For both of these problems, we investigate the asymptotic behav ior of the solutions as the distance from the finite end of a semi-inf inite cylinder tends to infinity and thus establish spatial decay resu lts of the Saint-Venant type.