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

Abstract

We consider the basin of the zero-solution to a semilinear parabolic equation on 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.

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Correspondence to Yasuhiro Fujita.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Fujita, Y. On basin of zero-solutions to a semilinear parabolic equation with Ornstein-Uhlenbeck operator. J Inequal Appl 2006, 52498 (2006). https://doi.org/10.1155/JIA/2006/52498

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  • DOI: https://doi.org/10.1155/JIA/2006/52498

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