Journal of Inequalities and Applications
Volume 2006 (2006), Article ID 52498, 10 pages
doi:10.1155/JIA/2006/52498
On basin of zero-solutions to a semilinear parabolic equation with Ornstein-Uhlenbeck operator
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.
Abstract
We consider the basin of the zero-solution to a semilinear parabolic equation on ℝN 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.