LIN Zhiqiang.Global existence and blow-up properties for quasilineardegenerate parabolic system[J].Journal of Yanbian University,2020,46(02):106-114.
拟线性退化抛物方程组解的存在性和爆破性
- Title:
- Global existence and blow-up properties for quasilinear degenerate parabolic system
- 文章编号:
- 1004-4353(2020)02-0106-09
- Keywords:
- nonlinear parabolic system; nonlocal source; uppe -lower solution; existence of global solutions; blow-up
- 分类号:
- O175.26
- 文献标志码:
- A
- 摘要:
- 讨论了具有Dirichlet边界条件的抛物型方程组{ut-div(|SymbolQC@ u|m -2 䥺SymbolQC@ u)=a1∫Ωup1dx ∫Ωvq1dx,vt-div(| 䥺SymbolQC@ v|n -2 䥺SymbolQC@ v)=a2∫Ωup2dx ∫Ωvq2dx解的性质.首先证明了该方程组解的局部存在唯一性,然后用上下解方法得到了该方程组解的整体存在和爆破的充分条件.
- Abstract:
- We consider the properties of solutions of quasilinear degenerate parabolic system {ut-div(| 䥺SymbolQC@ u|m -2· 䥺SymbolQC@ u)=a1∫Ωup1dx ∫Ωvq1dx, vt-div(| 䥺SymbolQC@ v|n -2 䥺SymbolQC@ v)=a2∫Ωup2dx ∫Ωvq2dx. Firstly we establish the local existence and uniqueness of solutions. Then by using lower -upper solution method, the sufficient conditions for the solutions of system that exist globally and blow -up in finite time are obtained.
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备注/Memo
收稿日期: 2020-03-03 基金项目: 福建省教育厅中青年教师教育科研项目(JT180741)
作者简介: 林志强(1983—),男,讲师,研究方向为偏微分方程.