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  

Global existence and blow-up for parabolic system with localized source

作　　者：林志强 LIN Zhiqiang(Fuzhou Institute of Technology,Fuzhou 350506,China)

机构地区：[1]福州理工学院,福建福州350506

出　　处：《延边大学学报（自然科学版）》2021年第1期10-16,共7页Journal of Yanbian University（Natural Science Edition）

基　　金：福建省教育厅中青年教师教育科研项目(JT180741)。

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(x0(t),t)+n v(x0(t),t),vt-(xβvx)x=ep u(x0(t),t)+q v(x0(t),t)的爆破性,其中x0(t)∶R+→(0,a)是Holder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.In this paper,we discuss the following weakly coupled degenerate and singular parabolic equations with localized source u t-(xαu x)x=e m u(x 0(t),t)+n v(x 0(t),t),v t-(xβv x)x=e p u(x 0(t),t)+q v(x 0(t),t)in(0,a)×(0,T)with homogeneous Dirichlet boundary conditions,where x 0(t)∶R+→(0,a)is Holder continuous,T≤∞,a(a>0)are constants,m,n,p,q are positive real numbers andα,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 conditionα=β.

关 键 词：上下解 局部化源 爆破 爆破集 爆破速率估计 

分 类 号：O175.26[理学—数学]