一类双重退化的奇异扩散方程 |
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引用本文: | 詹华税,;汤林冰.一类双重退化的奇异扩散方程[J].鹭江职业大学学报,2014(5):88-92. |
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作者姓名: | 詹华税 ;汤林冰 |
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作者单位: | [1] 厦门理工学院应用数学学院,福建 厦门361024; [2] 集美大学理学院,福建 厦门361021 |
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基金项目: | 国家自然科学基金项目(11371297) |
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摘 要: | 根据YIN和WANG的方法,结合Fichera-Oleinik理论,研究奇异扩散方程:φ( u)/t =div(ραu p-2u),(x,t)∈QT =Ωx(0,T),其中Ω是RN 中的有界区域,边界Ω充分光滑,ρ(x)=dist(x,Ω), p 〉1,α〉0,φ满足:φ∈C2,且存在δ〉0使得φ′(s)〉δ〉0.证明了α≥p -1时,不需要任何边值条件,方程最多有一个满足初值条件的解;而0〈α〈 p -1时,方程存在唯一满足初边值条件弱解.
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关 键 词: | 奇异扩散 弱解 Fichera-Oleinik理论 |
A Double Degenerate Singular Diffusion Equation |
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Institution: | ZHAN Hui-shui, TANG Lin-bing ( 1. School of Applied Mathematics, Xiamen University of Technology, Xiamen 361024, China; 2. School of Science, Jimei University, Xiamen 361021, China) ( 1. School of Applied Mathematics, Xiamen University of Technology, Xiamen 361024, China; 2. School of Science, Jimei University, Xiamen 361021, China) |
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Abstract: | The paper studies the singular diffusion equation in the method of YIN ’s and WANG ’s with Fichera-Oleinik theory:φ(u)/t = div(ρα u p-2 u),(x,t)∈QT = Ωx (0,T), whereΩis a bounded domain in RN with appropriately smooth boundaryΩ,ρ(x) = dist(x,Ω) , p 〉 1,α 〉 0 ,φ∈C2 , and there existsδ 〉0 such thatφ′( s) 〉 δ 〉0 . The paper proves that ifα≥p-1 , the equation admits a unique solution subject only to a given initial condition without any boundary condition, while if 0 〈 α 〈 p -1 , for a given initial condition, the equation admits different solutions for different boundary conditions. |
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Keywords: | singular diffusion weak solution Fichera-Oleinik theory |
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