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一类拟线性退化抛物方程的古典解

Classical Solution of a Quasilinear Degenerate Parabolic Equation
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摘要 对拟线性退化抛物方向xxu+uyu-tu=f(.,u),证明在(0,R)×(0,N)×(0,T)上初边值问题解存在唯一性,这里要求N充分小. The existence and uniqueness of the solution of the initial boundary problem for the following equation in Ω× （0,T）：axxu＋ugyu-atu=f（·,u）, is proved, where the N is small enough.
作者 李龙 詹华税
机构地区 集美大学理学院
出处 《集美大学学报（自然科学版）》 CAS 2010年第2期142-146,共5页 Journal of Jimei University：Natural Science
基金 福建省自然科学基金资助项目(T0650010) 集美大学科研基金资助项目(C60416)
关键词 退化抛物方程 初边值问题 存在唯一性 degenerate parabolic equation initial boundary problem existence uniqueness
分类号 O175.29 [理学—基础数学]
  • 相关文献

参考文献6

  • 1ANTONELLI F, BATRUCCI E, MANCINO M E. A comparison result for BFSDE's and applications to decisions theory [J]. Math Methods Opwer Res, 2001, 54: 407-423.
  • 2GRANDALL M G, ISHII H, LIONS P L. User's guide to viscosity solutions of second order partial differential equations [J]. Bull Amer Math Soc (N. S), 1992, 27: 1-67.
  • 3ANTONELLI F, PASCUCCI A. On the viscosity solutions of a stochastic differential utility problem [J]. J Differ Equations, 2002, 186: 901-918.
  • 4ESXOBED M, VAZQUEZ J L, ZUAZUA E. Entropy solutions for diffusion-convection equations with partial diffusivity [J]. Trans Amer Soc, 1994, 343(2) : 829-842.
  • 5詹华税.关于一类拟线性退化抛物方程[J].数学年刊（A辑）,2006,27(6):731-740. 被引量：5
  • 6OLEINIK 0 A, SAMOKGIN V N. Mathematical models in boundary layer theory [M]. New York: Chapman and Hall/ CRC, 1999.

二级参考文献10

  • 1Antonelli F.,Batrucci E.and Mancino M.E.,A comparison result for BFSDE's and applications to decisions theory[J],Math.Methods Opwer.Res.,2001,54:407-423.
  • 2Crandall M.G.,Ishii H.and Lions P.L.,User's guide to viscosity solutions of second order partial differential equations[J],Bull.Amer.Math.Soc.(N.S.),1992,27:1-67.
  • 3Antonelli F.and Pascucci A.,On the viscosity solutions of a stochastic differential utility problem[J],J.Differ.Equations,2002,186:69-87.
  • 4Citti G.,Pascucci A.and Polidoro S.,Regularity properties of viscosity solutions of a non-H(o)rmander degenerate equation[J],J.Math.Pures Appl.,2001,80(9):901-918.
  • 5Esxobedo M.,Vazquez J.L.and Zuazua E.,Entropy solutions for diffusion-convection equations with partial diffusivity[J],Trans.Amer.Math.Soc.,1994,343(2):829-842.
  • 6Oleinik O.A.and Samokgin V.N.,Mathematical Models in Boundary Layer Theory[M],Boca Roton,London,New York,Washington D.C.:Chapman and Hail/CRC,1999.
  • 7Citti G.,Pascucci A.and Polidoro S.,On the regularity properties of viscosity solutions of a nonlinear ultraparabolic equation arising in mathematical finance[J],Differ.Inter.Equ.,2001,14(6):701-738.
  • 8Zhan H.,The study of the Cauchy problem of a second order quasilinear degenerate parabolic equation and the parallelism of a Riemannian manifold[D],Doctor Thesis,Xiamen University,2004.
  • 9Chen G.Q.and Perthame B.,Well-posedness for non-isotropic degenerate parabolic-hyperbolic equations[J],Ann.I.H.Poincare-AN,2003,20(4):645-668.
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共引文献4

集美大学学报（自然科学版）
2010年 第2期

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