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Global existence and blow-up of solutions to reaction-diffusion system with a weighted nonlocal source
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作者 蒋良军 王悦生 《Journal of Shanghai University(English Edition)》 CAS 2011年第6期501-505,共5页
In this paper,we study a semi-linear reaction-diffusion system with a weighted nonlocal source,subject to the null Dirichlet boundary condition.Under certain conditions,we prove that the classical solution exists glob... In this paper,we study a semi-linear reaction-diffusion system with a weighted nonlocal source,subject to the null Dirichlet boundary condition.Under certain conditions,we prove that the classical solution exists globally and blows up in finite time respectively,and then obtain the uniform blow-up rate in the interior. 展开更多
关键词 reaction-diffusion system nonlocal source uniform blow-up profile weight function simultaneous blow-up
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The Proof of the Sufficient and Necessary Conditions which Make the Hausdorff Measure of the Generalized Non-uniform Cantor Set'exist
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作者 ZENG Chao-yi 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2006年第2期293-296,共4页
The paper succeeds in the obtaining a class of generalized non-uniform Cantor set based on the iteration (1): Si(x) = αix + bi, x ∈ [0, 1], i = 1,2,…, m, where 0 〈 αi 〈 1, i = 1,2,…,m; bi + αi 〉 0, i =... The paper succeeds in the obtaining a class of generalized non-uniform Cantor set based on the iteration (1): Si(x) = αix + bi, x ∈ [0, 1], i = 1,2,…, m, where 0 〈 αi 〈 1, i = 1,2,…,m; bi + αi 〉 0, i = 1,2,…,m- 1, b1 = 0 and αm + bm = 1. Providing the sufficient and necessary conditions of its existence Hausdorff measure. 展开更多
关键词 self-similar set Cantor set Hausdorff dimension Hausdorff measure
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2π-periodic Solution for a Kind High Order Delay Duffing Equation 被引量:4
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作者 LIN Wen-xian 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2006年第1期85-89,共5页
In this paper, the high order delay Duffing equation ax^(2n) +bx+g(x(t-r)) = p(t) are considered,using the theory of coincidence degree, the sufficient condition for its there being at least a 2π-periodic s... In this paper, the high order delay Duffing equation ax^(2n) +bx+g(x(t-r)) = p(t) are considered,using the theory of coincidence degree, the sufficient condition for its there being at least a 2π-periodic solution is obtained. 展开更多
关键词 Duffing equation periodic solution coincidence degree
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Topological r-entropy and measure-theoretic r-entropy of a continuous map 被引量:5
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作者 REN YunLi HE LianFai +1 位作者 LV JinFeng ZHENG GuoPing 《Science China Mathematics》 SCIE 2011年第6期1197-1205,共9页
In this paper,we introduce the concept of measure-theoretic r-entropy of a continuous map on a compact metric space,and get the results as follows:1.Measure-theoretic entropy is the limit of measure-theoretic r-entrop... In this paper,we introduce the concept of measure-theoretic r-entropy of a continuous map on a compact metric space,and get the results as follows:1.Measure-theoretic entropy is the limit of measure-theoretic r-entropy and topological entropy is the limit of topological r-entropy(r → 0);2.Topological r-entropy is more than or equal to the supremum of 4r-entropy in the sense of Feldman's definition,where the measure varies among all the ergodic Borel probability measures. 展开更多
关键词 topological r-entropy measure-theoretic r-entropy
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Asymptotic Analysis to a Diffusion Equation with a Weighted Nonlocal Source
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作者 JIANG Liang-jun 《Chinese Quarterly Journal of Mathematics》 2015年第2期244-252,共9页
In this paper,we deal with the blow-up property of the solution to the diffusion equation u_t = △u + a(x)f(u) ∫_Ωh(u)dx,x∈Ω,t>0 subject to the null Dirichlet boundary condition.We will show that under certain ... In this paper,we deal with the blow-up property of the solution to the diffusion equation u_t = △u + a(x)f(u) ∫_Ωh(u)dx,x∈Ω,t>0 subject to the null Dirichlet boundary condition.We will show that under certain conditions,the solution blows up in finite time and prove that the set of all blow-up points is the whole region.Especially,in case of f(s) = s^p,h(s) = s^q,0 ≤ p≤1,p + q >1,we obtain the asymptotic behavior of the blow up solution. 展开更多
关键词 asymptotic analysis diffusion equation global blow-up nonlocal sources weight function
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