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Hodograph-Type Transformations for Linearization of Systems of Nonlinear Diffusion Equations

文献类型：期刊论文

作者Kang, Jing2,3; Qu, Changzheng1
刊名STUDIES IN APPLIED MATHEMATICS
出版日期2010-04-01
卷号124页码:247-281
ISSN号0022-2526
DOI10.1111/j.1467-9590.2009.00470.x
英文摘要In this paper, we study the problem of linearization of nonlinear systems of equations u(t) = f(u(x), v(x))u(xx) + p(u(x), v(x))v(xx), v(t) = g(u(x), v(x))v(xx) + q(u(x), v(x))u(xx), which is a potential form of systems of nonlinear diffusion equations u(t) = (f(u, v)u(x) + p(u, v)v(x)x), v(t) = (g(u, v)v(x) + q(u, v)u(x)x). We construct a class of point transformations of the form t' = t, x' = X(u, v), u' = R(x, u, v), v' = S(x, u, v) which connects the nonlinear systems with linear systems of equations u'(t') = au'(x'x') + b nu'(x'x'), v'(t') = c nu'(x'x') + du'(x'x'). These point transformations are hodograph-type transformations which have the property that the new independent and dependent variables depend, respectively, on the old dependent and independent variables. All systems of equations admitting such transformations are completely classified.
WOS关键词PARTIAL-DIFFERENTIAL-EQUATIONS ; EVOLUTION-EQUATIONS ; POTENTIAL SYMMETRIES ; COUPLED DIFFUSION ; CLASSIFICATION ; HIERARCHIES
资助项目China NSF[10925104] ; Science Foundation of Northwest University[NO09NW20]
WOS研究方向Mathematics
语种英语
WOS记录号WOS:000276273700003
出版者WILEY-BLACKWELL
资助机构China NSF ; Science Foundation of Northwest University
源URL[http://119.78.100.186/handle/113462/32271]  
专题中国科学院近代物理研究所
通讯作者Qu, Changzheng
作者单位1.NW Univ Xian, Inst Modern Phys, Xian 710069, Peoples R China
2.NW Univ Xian, Ctr Nonlinear Studies, Xian 710069, Peoples R China
3.NW Univ Xian, Dept Math, Xian 710069, Peoples R China
推荐引用方式
GB/T 7714		 Kang, Jing,Qu, Changzheng. Hodograph-Type Transformations for Linearization of Systems of Nonlinear Diffusion Equations[J]. STUDIES IN APPLIED MATHEMATICS,2010,124:247-281.
APA Kang, Jing,&Qu, Changzheng.(2010).Hodograph-Type Transformations for Linearization of Systems of Nonlinear Diffusion Equations.STUDIES IN APPLIED MATHEMATICS,124,247-281.
MLA Kang, Jing,et al."Hodograph-Type Transformations for Linearization of Systems of Nonlinear Diffusion Equations".STUDIES IN APPLIED MATHEMATICS 124(2010):247-281.

入库方式： OAI收割

来源：近代物理研究所

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