工程数学学报
工程數學學報
공정수학학보
CHINESE JOURNAL OF ENGINEERING MATHEMATICS
2009年
3期
397-406
,共10页
推广旋转群%推广伸缩群%精确解%非线性扩散方程
推廣鏇轉群%推廣伸縮群%精確解%非線性擴散方程
추엄선전군%추엄신축군%정학해%비선성확산방정
extended rotation group%extended scaling group%exact solution%nonlinear diffusion equation
本文研究非线性扩散方程的精确解,文中分别给出非线性扩散方程在推广旋转群和推广伸缩群上不变时满足的条件,并且利用推广旋转群和推广伸缩群构造方程的精确解,最后,给出了非线性扩散方程在推广旋转伸缩群上不变时满足的条件,推广旋转伸缩群也被用来构造非线性扩散方程的精确解.
本文研究非線性擴散方程的精確解,文中分彆給齣非線性擴散方程在推廣鏇轉群和推廣伸縮群上不變時滿足的條件,併且利用推廣鏇轉群和推廣伸縮群構造方程的精確解,最後,給齣瞭非線性擴散方程在推廣鏇轉伸縮群上不變時滿足的條件,推廣鏇轉伸縮群也被用來構造非線性擴散方程的精確解.
본문연구비선성확산방정적정학해,문중분별급출비선성확산방정재추엄선전군화추엄신축군상불변시만족적조건,병차이용추엄선전군화추엄신축군구조방정적정학해,최후,급출료비선성확산방정재추엄선전신축군상불변시만족적조건,추엄선전신축군야피용래구조비선성확산방정적정학해.
In this paper, we study exact solutions to nonlinear diffusion equations. We formulate conditions for the nonlinear diffusion equation which is invariant under the extended rotation group and the extended scaling group, respectively. Meanwhile, we construct exact solutions to nonlinear diffusion equations by using the extended rotation group and the extended scaling group. Finally, we formulate conditions for nonlinear diffusion equation which is invariant under the extended rotation-scaling group, the extended rotation-scaling group is also used to construct exact solutions to the nonlinear diffusion equation.