Uniform blow-up rate for parabolic equations with a weighted nonlocal nonlinear source |
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Authors: | Liangjun Jiang Yongping Xu |
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Affiliation: | a Department of Mathematics, Nanjing XiaoZhuang College, Nanjing 211171, PR China b College of Information Sciences and Technology, Nanjing Forestry University, Nanjing 210037, PR China |
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Abstract: | In this paper, the blow-up rate of solutions of semi-linear reaction-diffusion equations with a more complicated source term, which is a product of nonlocal (or localized) source and weight function a(x), is investigated. It is proved that the solutions have global blow-up, and that the rates of blow-up are uniform in all compact subsets of the domain. Furthermore, the blow-up rate of ∞|u(t)| is precisely determined. |
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Keywords: | Semi-linear diffusion equation Uniform blow-up rate Nonlocal sources Weight function |
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