Singular properties of solutions for a parabolic equation with variable exponents and logarithmic source期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Singular properties of solutions for a parabolic equation with variable exponents and logarithmic source

Institution:	1. Faculty of Mathematics and Applications, Saigon University, Ho Chi Minh City, Viet Nam;2. Department of Mathematics and Statistics, University of Economics Ho Chi Minh City, Viet Nam;3. Faculty of Fundamental Sciences, University of Architecture Ho Chi Minh City, Viet Nam

Abstract:	This paper deals with a parabolic $p (x)$ -Laplace equation with logarithmic source $u^{q (x)} log u$ . The singular properties of solutions are determined completely by classifying the initial energy. Moreover, we obtain a new extinction rate of solutions, where the order of the extinction rate is greater than the maximum of variable exponent $q (x)$ . This kind of extinction rate could reflect the influence of logarithmic functions on the extinction of solutions more reasonably.

Keywords:	Variable exponent Blow-up Extinction Global existence Initial energy
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