[1]张康群,孙福树,赵国俊.一类半线性Keldysh型方程解的注记[J].南京师范大学学报(自然科学版),2013,36(02):5-9.
 Zhang Kangqun,Sun Fushu,Zhao Guojun.A Note on the Solution of a Class of Keldysh-Type Equations[J].Journal of Nanjing Normal University(Natural Science Edition),2013,36(02):5-9.
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一类半线性Keldysh型方程解的注记()
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《南京师范大学学报》(自然科学版)[ISSN:1001-4616/CN:32-1239/N]

卷:
第36卷
期数:
2013年02期
页码:
5-9
栏目:
数学
出版日期:
2013-06-30

文章信息/Info

Title:
A Note on the Solution of a Class of Keldysh-Type Equations
文章编号:
1001-4616(2013)02-0005-05
作者:
张康群孙福树赵国俊
南京工程学院数理部,江苏 南京 21116
Author(s):
Zhang KangqunSun FushuZhao Guojun
Department of Mathematics and Physics,Nanjing Institute of Technology,Nanjing 211167,China
关键词:
Keldysh型方程初值问题存在性奇性传播
Keywords:
Keldysh-type equationinitial value problemexistensesingularity propogation
分类号:
O175.28
文献标志码:
A
摘要:
Keldysh方程是在研究跨音速管道流问题时导出的一个简化的数学模型,也是研究混合型偏微分方程模型的一个典型代表.对于其含有非零源项的退化双曲部分的初值问题,本文利用部分Fourier变换与ODE求解的办法给出了相应线性方程解的一个显式表达式及其全局一致估计,并在这个估计的基础上利用不动点定理建立了一类半线性问题的解的全局存在性.同时给出了解的奇性传播可以仅沿一支特征线传播的一个例子.
Abstract:
Keldysh equation is a mathematical model which was derived in studying fluid dynamics,and also is a typical example of mixed type partial differential equations.For the initial value problem of its degenerate hyperbolic part with nonzero source term,we find a solution by use of partial Fourier transformation and ODE’s method,and then derive its a global uniform estimate.Based on it and the fixed point theorem,we establish the global existence for solution of a class of semilinear problem.Meanwhile,we find an example to desmontrate the propogation of singularity which is only along one of the characteristics.

参考文献/References:

[1] Yagdjian K.Global existence for the n-dimensional semilinear Tricomi-type equations[J].Comm Partial Differential Equations,2006,31(4/6):907-944.
[2]Zhang Kangqun.Existence and regularity of solution to the generalized Tricomi equation with a singular initial datum at a point[J].Acta Math Sinica,2011,28(6):1 135-1 154.
[3]Chen Shuxing.The fundamental solution of the Keldysh type operator[J].Science in China Series A:Mathematics,2009,52(9):1 829-1 843.
[4]Sun(ˇoverc)ica(ˇoverC)anic,Barbara Lee Keyfitz.A smooth solution for a keldysh type equation[J].Communications in Partial Differential Equations,1996,21(1/2):319-340.
[5]Qi Minyou.On the Cauchy problem for a class of hyperbolic equations with initial data on the parabolic degenerating line[J].Acta Math Sinica,1958,8:521-529.
[6]Zhang Kangqun.Existence of solution for the n-dimensional semilinear Tricomi-type equations[J].Comm Partial Differential Equations,2006,31(4/6):907-944.
[2]Zhang Kangqun.Existence and regularity of solution to the generalized Tricomi equation with a singular initial datum at a point[J].Acta Math Sinica,2011,28(6):1 135-1 154.
[3]Chen Shuxing.The fundamental solution of the Keldysh type operator[J].Science in China Series A:Mathematics,2009,52(9):1 829-1 843.
[4]Sun(ˇoverc)ica(ˇoverC)anic,Barbara Lee Keyfitz.A smooth solution for a keldysh type equation[J].Communications in Partial Differential Equations,1996,21(1/2):319-340.
[5]Qi Minyou.On the Cauchy problem for a class of hyperbolic equations with initial data on the parabolic degenerating line[J].Acta Math Sinica,1958,8:521-529.
[6]Zhang Kangqun.Existence of solution for the mension second order semilinear hyperbolic equations[J].Journal of Mathematical Analysis and Applications,2011,381(1):427-440.
[7]Erdelyi A,Magnus W,Oberhettinger F,et al.Higher Transcendental Functions[M].New York,Toronto,London:McGraw-Hill Book Company,1953.

备注/Memo

备注/Memo:
收稿日期:2013-01-20.
基金项目:国家自然科学基金(11001122)、南京工程学院科研基金(YKJ201113、QKJC2010013).
通讯联系人:张康群,博士,讲师,研究方向:偏微分方程.E-mail:chkqnju@hotmail.com
更新日期/Last Update: 2013-06-30