Existence and decay estimates for time dependent parabolic equation with application to Duncan-Mortensen-Zakai equation
type: Item
instance of: scholarly article
title: Existence and decay estimates for time dependent parabolic equation with application to Duncan-Mortensen-Zakai equation
zbMATH Open document ID: 0953.35052
published in: The Asian Journal of Mathematics
publication date: 2000-11-15T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 35K10
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 93E20
Mathematics Subject Classification ID: 35B05
zbMATH DE Number: 1531013
zbMATH Keywords: positive solution
author: Shing-Tung Yau
author: Stephen Yau
reviewed by: Luis Alberto Fernández
MaRDI profile type: Publication
full work available at URL: ajm.1998.v2.n4.a17
OpenAlex ID: W2741850185
DOI: 10.4310/AJM.1998.V2.N4.A17
description: scientific article; zbMATH DE number 1531013