Finite time blow-up for a class of parabolic or pseudo-parabolic equations |
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Authors: | Fenglong Sun Lishan Liu Yonghong Wu |
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Affiliation: | 1. School of Mathematical Sciences, Qufu Normal University, Qufu 273165, Shandong, People’s Republic of China;2. Department of Mathematics and Statistics, Curtin University, Perth, WA 6845, Australia |
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Abstract: | In this paper, we study the initial boundary value problem for a class of parabolic or pseudo-parabolic equations: where , with being the principal eigenvalue for on and . By using the potential well method, Levine’s concavity method and some differential inequality techniques, we obtain the finite time blow-up results provided that the initial energy satisfies three conditions: (i) ; (ii) , where is a nonnegative constant; (iii) , where involves the -norm or -norm of the initial data. We also establish the lower and upper bounds for the blow-up time. In particular, we obtain the existence of certain solutions blowing up in finite time with initial data at the Nehari manifold or at arbitrary energy level. |
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Keywords: | Parabolic equation Pseudo-parabolic equation Concavity method Blow-up Life span |
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