一类具有非线性边界流的双重退化抛物方程组解的整体存在与爆破(英文)  

Global Existence and Blow-up of Solutions to a Class of Doubly Degenerate Parabolic Equations Coupled via Nonlinear Boundary Flux

作　　者：米永生[1,2] 穆春来[2] 

机构地区：[1]长江师范学院数学与计算机学院,重庆408100 [2]重庆大学数学与统计学院,重庆401331

出　　处：《数学进展》2014年第3期398-410,共13页Advances in Mathematics（China）

基　　金：supported by NSFC(No.11371384);NSF of Chongqing(No.cstc2013jcyjA0940);NSF of Fuling(No.FLKJ2013ABA2036)

摘　　要：研究一类具有非线性边界流的双重退化抛物方程组解的临界指数,通过构造自相似的上下解,得到了整体存在曲线.借助一些新的结果,获得了Fujita临界指数.其中一个有趣的现象是:整体存在曲线和Fujita临界曲线分别是由一个矩阵和一个线性方程组的解来决定.The paper deals with the critical curve for a degenerate parabolic system coupled via nonlinear boundary flux. By constructing the self-similar super-solution and sub- solution, we obtain the critical global existence curve, and the critical curve of Fujita type is conjectured with the aid of some new results. An interesting feature of our results is that the critical global existence curve and the critical Fujita curve are determined by a matrix and by the solution of a linear algebraic system, respectively.

关 键 词：整体存在曲线 退化抛物方程组 临界Fujita曲线 非线性边界流 爆破 

分 类 号：O175.26[理学—数学]