Journal of Inequalities and Applications
Volume 2006 (2006), Article ID 52498, 10 pages

On basin of zero-solutions to a semilinear parabolic equation with Ornstein-Uhlenbeck operator

Yasuhiro Fujita

Department of Mathematics, Toyama University, Toyama 930-8555, Japan

Received 27 April 2005; Accepted 10 July 2005

Copyright © 2006 Yasuhiro Fujita. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider the basin of the zero-solution to a semilinear parabolic equation on N with the Ornstein-Uhlenbeck operator. Our aim is to show that the Ornstein-Uhlenbeck operator contributes to enlargement of the basin by using the logarithmic Sobolev inequality.