Blow-up solutions and global solutions for nonlinear parabolic problems |
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| Institution: | 1. Department of Mathematics, Tamkang University, 151, Yingzhuan Road, Tamsui, New Taipei City 25137, Taiwan;2. Université Paris 13, Sorbonne Paris Cité, Laboratoire Analyse, Géométrie et Applications, CNRS (UMR 7539), 93430 Villetaneuse, France;1. Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong;2. School of Mathematical Sciences, University of Electronic Science & Technology of China, Chengdu 611731, PR China;1. College of Management and Economics, Tianjin University, Tianjin, 300072, PR China;2. Department of Basic Curriculum, The Chinese People’s Armed Police Force Academy, Lang Fang, He Bei, 065000, PR China;3. Department of Mathematics, School of Mathematics, Tianjin University, Tianjin, 300072, PR China;1. School of Mathematics and Statistics, Shandong Normal University, Jinan, Shandong, 250358, China;2. School of Mathematical Sciences and LPMC, Nankai University, Tianjin, 300071, China;3. School of Mathematical Sciences, Nankai University, Tianjin, 300071, China |
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| Abstract: | This paper deals with the blow-up of positive solutions for a nonlinear parabolic equation subject to nonlinear boundary conditions. We obtain the conditions under which the solutions may exist globally or blow up in a finite time, by a new approach. Moreover, upper estimates of the “blow-up time”, blow-up rate and global solutions are obtained also. |
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