拟线性退化抛物方程Cauchy问题的解  

Solutions to the Cauchy Problem of a Quasilinear Degenerate Parabolic Equation

作　　者：詹华税[1] 

机构地区：[1]集美大学理学院,福建厦门361021

出　　处：《数学年刊（A辑）》2012年第4期449-460,共12页Chinese Annals of Mathematics

基　　金：福建省自然科学基金(No.2009J01009);集美大学潘金龙科学基金(No.ZC2010019)资助的项目

摘　　要：对来自金融数学领域的方程_(xx)u+u_yu-_tu=c(x,y,t,u),(x,y,t)∈Q_T=R^2×[0,T)的Cauchy问题,给出了一种新的熵解的定义,得到了其适定性结果.可以证明所得到的解还是强解,即方程中所出现的各阶偏导数几乎处处连续.最后讨论了解的爆破性质以及与解的间断点相关的几何性质.The paper gives a new definition of the BV-solution to the Cauchy problem of the following equation coming from finance mathematics：δxxu＋uδyu-δtu=c（x,y,t,u）, （x,y,t）∈QT=R^2×[0,T]的Cauchy and gets its well-posedness. Moreover, it can be proved that this solution is a strong solution, which means all the partial derivatives emerging in the equation are almost everywhere continuous in QT. At the same time, the blow-up phenomena of the solutions and the geometrical properties of the jump points of the solutions are discussed.

关 键 词：退化抛物方程 熵解 CAUCHY问题 爆破 强解 

分 类 号：O175.26[理学—数学]