LIN Zhiqiang.Global existence and blow-up for parabolic system with localized source[J].Journal of Yanbian University,2021,47(01):10-16.
带有局部化源的弱耦合退化奇异抛物型方程组解的爆破性
- Title:
- Global existence and blow-up for parabolic system with localized source
- 文章编号:
- 1004-4353(2021)01-0010-07
- Keywords:
- upper and lower solutions; localized source; blow -up; blow -up set; blow -up rate estimates
- 分类号:
- O175.26
- 文献标志码:
- A
- 摘要:
- 在齐次狄利克雷边界条件下讨论了带有局部化源的弱耦合退化奇异抛物型方程组ut-(xαux)x=em u(x<sup>0(t),t)+n v(x<sup>0(t),t), vt-(xβvx)x=ep u(x<sup>0(t),t)+q v(x<sup>0(t),t)的爆破性,其中x0(t):R+→(0,a)是Hölder连续的, T≤∞, a(a>0)是常数, m、n、p、q是正实数, α,β∈[0,2).利用上下解的方法得到了上述方程组的非负古典解的存在性和解在有限时刻爆破的充分条件,并得到了α=β条件下的解的爆破速率.
- Abstract:
- In this paper, we discuss the following weakly coupled degenerate and singular parabolic equations with localized source ut-(xαux)x=em u(x<sup>0(t),t)+n v(x<sup>0(t),t), vt-(xβvx)x=ep u(x<sup>0(t),t)+q v(x<sup>0(t),t) in(0,a)×(0,T)with homogeneous Dirichlet boundary conditions, where x0(t):R+→(0,a)is Hölder continuous, T≤∞, a(a>0)are constants, m,n,p,q are positive real numbers and α,β∈[0,2). The existence of a unique classical non -negative solution is established and the sufficient conditions for the solution that blow -up in finite time are obtained. We also obtain the blow -up rate under the condition α=β.
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备注/Memo
收稿日期: 2020-09-20
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.