Existence and decay estimates for time dependent parabolic equation with application to Duncan-Mortensen-Zakai equation (Q1585460)

This work provides the existence of a positive solution for an evolution equation of the type \[ \partial u/\partial t = \Delta u + \sum_{i=1}^n f_i \partial u/\partial x_{i} - V u. \] Moreover, very precise decay estimates for the solution are derived under reasonable assumptions on \(f_i\) and \(V\) in applications: concretely, the differentiation with respect to time of these terms has been avoided. Finally, the Duncan-Mortensen-Zakai equation is treated.