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Hamilton-Jacobi方程特征线的性质Ⅰ(英文) 被引量：1

Properties of the Charactristic of Hamilton-Jacobi Equations Ⅰ
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摘要 研究带凸Hamiltonian的高维Hamilton-Jacobi(HJ)方程特征线的性质.证明了HJ方程解的表达式中的极值曲线是特征线,对上半空间中任一点,都存在1条有效特征线段经过它. This paper is concerned with the Hamilton-Jacobi(HJ) equations of multidimensional space variables with convex Hamiltonians.The author proves the extreme curve in the formula of the solution to the HJ equation is a characteristic and for each point in upper half-space,there exists a valid characteristic segment passing through it.
作者 赵引川
机构地区 华北电力大学数理系
出处 《吉首大学学报（自然科学版）》 CAS 2010年第1期13-15,共3页 Journal of Jishou University(Natural Sciences Edition)
基金 National Natural Foundation of China(10926067 70901025)
关键词 HAMILTON-JACOBI方程 特征线 Hopf-Lax公式 Hamilton-Jacobi equation characteristic Hopf-Lax formula
分类号 O175 [理学—基础数学]
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参考文献8

  • 1赵引川.Hamilton-Jacobi方程特征线的性质Ⅰ(英文)[J].吉首大学学报（自然科学版）,2010,31(1):13-15. 被引量：1
  • 2BARDI M,EVANS L C.On Hopf‘‘‘‘s Formulas for Solutions of Hamilton-Jacobi Equations. Nonlinear Anal.Theory,Meth-ods&Applications . 1984
  • 3HOPF E.Generalized Solutions of Nonlinear Equations of First Order. Math.Mech . 1965
  • 4ZHAO Y,TANG T,WANG J.Regularity and Global Structure of Solutions to Hamilton-Jacobi Equations II.ConvexInitial Data. J.Hyperbol.Differ.Eq . 2009
  • 5SCHAEFFER D G.A regularity theorem for conversation laws. Advances in Mathematics . 1973
  • 6Li B,Wang J.The global qualitative study of solutions to a conservation law (I). Mathematics in Computer Science . 1979
  • 7ZHAO Y,TANG T,WANG J.Regularity and Global Structure of Solutions to Hamilton-Jacobi Equations I.ConvexHamiltonians. J.Hyperbol.Differ.Eq . 2008
  • 8Tang T,Wang J,Zhao Y.On the piecewise smoothness of entropy solutions to scalar conservation laws for larger class of initial data. J Hyperbolic Differ Equ . 2007

二级参考文献8

  • 1赵引川.Hamilton-Jacobi方程特征线的性质Ⅰ(英文)[J].吉首大学学报（自然科学版）,2010,31(1):13-15. 被引量：1
  • 2BARDI M,EVANS L C.On Hopf‘‘‘‘s Formulas for Solutions of Hamilton-Jacobi Equations. Nonlinear Anal.Theory,Meth-ods&Applications . 1984
  • 3HOPF E.Generalized Solutions of Nonlinear Equations of First Order. Math.Mech . 1965
  • 4ZHAO Y,TANG T,WANG J.Regularity and Global Structure of Solutions to Hamilton-Jacobi Equations II.ConvexInitial Data. J.Hyperbol.Differ.Eq . 2009
  • 5SCHAEFFER D G.A regularity theorem for conversation laws. Advances in Mathematics . 1973
  • 6Li B,Wang J.The global qualitative study of solutions to a conservation law (I). Mathematics in Computer Science . 1979
  • 7ZHAO Y,TANG T,WANG J.Regularity and Global Structure of Solutions to Hamilton-Jacobi Equations I.ConvexHamiltonians. J.Hyperbol.Differ.Eq . 2008
  • 8Tang T,Wang J,Zhao Y.On the piecewise smoothness of entropy solutions to scalar conservation laws for larger class of initial data. J Hyperbolic Differ Equ . 2007

同被引文献7

  • 1BARDI M,EVANS L C.On Hopf‘‘‘‘s Formulas for Solutions of Hamilton-Jacobi Equations. Nonlinear Anal.Theory,Meth-ods&Applications . 1984
  • 2HOPF E.Generalized Solutions of Nonlinear Equations of First Order. Math.Mech . 1965
  • 3ZHAO Y,TANG T,WANG J.Regularity and Global Structure of Solutions to Hamilton-Jacobi Equations II.ConvexInitial Data. J.Hyperbol.Differ.Eq . 2009
  • 4SCHAEFFER D G.A regularity theorem for conversation laws. Advances in Mathematics . 1973
  • 5Li B,Wang J.The global qualitative study of solutions to a conservation law (I). Mathematics in Computer Science . 1979
  • 6ZHAO Y,TANG T,WANG J.Regularity and Global Structure of Solutions to Hamilton-Jacobi Equations I.ConvexHamiltonians. J.Hyperbol.Differ.Eq . 2008
  • 7Tang T,Wang J,Zhao Y.On the piecewise smoothness of entropy solutions to scalar conservation laws for larger class of initial data. J Hyperbolic Differ Equ . 2007

引证文献1

二级引证文献1

吉首大学学报（自然科学版）
2010年 第1期

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