带非局部源的退化奇异半线性抛物方程组解的存在性和爆破  

Blow-up for Degenerate and Singular Semilinear Parabolic Systems with Nonlocal Source

作　　者：陆求赐[1] 曾有栋[2] 

机构地区：[1]南平师范高等专科学校基础教育系,福建南平353000 [2]福州大学数学系,福州350002

出　　处：《西南师范大学学报（自然科学版）》2006年第6期15-19,共5页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：福建省自然科学基金资助项目(Z0511015)

摘　　要：主要研究带有Dirichlet边界条件的非局部退化半线性抛物方程组ut-(xαux)x=∫0ag(v)dxvt-(xαvx)x=∫0af(u)dx在(0,a)×(0,T)内正解的爆破性质.证明了古典解的存在性与唯一性,并得到当初值充分大时,解在有限时刻爆破.This paper deals with the blow-up properties of the positive solutions to the nonlocal degenerate and singular semilinear parabolic system u_t-(x~αu_x)_x=∫~a_0g(v)dx,v_t-(x~αv_x)_x=∫~a_0f(u)dx in(0,a)×(0,T) with homogeneous Dirichlet boundary conditions.The existence and uniqueness of classical solutions are proved.It is also obtained that the solutions is blowing-up in finite time when initial value is sufficiently large.

关 键 词：非局部源 退化奇异方程组 爆破 存在性与唯一性 

分 类 号：O175.26[理学—数学]