Blow-up of p-Laplacian evolution equations with variable source power

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• 作者：Zhi Zheng ; YuanWei Qi ; ShuLin Zhou
• 关键词：p ; Laplacian ; blow ; up ; variable source power
• 刊名：Science China Mathematics
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：60
• 期：3
• 页码：469-490
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Applications of Mathematics;
• 出版者：Science China Press
• ISSN：1869-1862
• 卷排序：60

文摘

We study the blow-up and/or global existence of the following p-Laplacian evolution equation with variable source power $${s_j} = {\beta _j} + \overline {{\beta _{n - j}}}p$$ where Ω is either a bounded domain or the whole space ℝ^{N, q(x) is a positive and continuous function defined in Ω with 0 < q₋ = inf q(x) ⩽ q(x) ⩽ sup q(x) = q+ < ∞. It is demonstrated that the equation with variable source power has much richer dynamics with interesting phenomena which depends on the interplay of q(x) and the structure of spatial domain Ω, compared with the case of constant source power. For the case that Ω is a bounded domain, the exponent p − 1 plays a crucial role. If q+ > p − 1, there exist blow-up solutions, while if q₊ < p − 1, all the solutions are global. If q₋ > p − 1, there exist global solutions, while for given q₋ < p − 1 < q₊, there exist some function q(x) and Ω such that all nontrivial solutions will blow up, which is called the Fujita phenomenon. 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J Differential Equations, 1995, 121: 329–383CrossRefMATHGoogle ScholarCopyright information© Science China Press and Springer-Verlag Berlin Heidelberg 2016Authors and AffiliationsZhi Zheng1YuanWei Qi2Email authorShuLin Zhou11.School of Mathematical SciencesPeking UniversityBejingChina2.Department of MathematicsUniversity of Central FloridaOrlandoUSA About this article CrossMark Publisher Name Science China Press Print ISSN 1674-7283 Online ISSN 1869-1862 About this journal Reprints and Permissions Article actions .buybox { margin: 16px 0 0; position: relative; } .buybox { font-family: Source Sans Pro, Helvetica, Arial, sans-serif; font-size: 14px; font-size: .875rem; } .buybox { zoom: 1; } .buybox:after, .buybox:before { content: ''; display: table; } .buybox:after { clear: both; } /*---------------------------------*/ .buybox .buybox__header { border: 1px solid #b3b3b3; border-bottom: 0; padding: 8px 12px; position: relative; background-color: #f2f2f2; } .buybox__header .buybox__login { font-family: Source Sans Pro, Helvetica, Arial, sans-serif; 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