J4 ›› 2010, Vol. 48 ›› Issue (06): 877-881.

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Exact Solutions to 2Dimensional Parabolic MongeAmpèreEquations with Source Term

ZHAO Pengfei1,2, LI Hengyan3, LIU Dong4   

  1. 1. College of Geoexploration Science and Technology, Jilin University, Changchun 130061, China;2. PostDoctoral Flow Station of Computer Science and Technology, Jilin University, Changchun 130012, China;3. Institute of Mathematics, Jilin |University, Changchun 130012, China;4. College of Mathematics, Jilin University, Changchun 130012, China
  • Received:2010-01-22 Online:2010-11-26 Published:2010-11-26
  • Contact: ZHAO Pengfei E-mail:zhaopengfei1981@yahoo.cn

Abstract:

We used the invariant set method to solve the 2-dimensional parabolic MongeAmpère equation with source term ut=det D2u+P(u) in R2 and the generalized 2-dimensional parabolic Monge-Ampère equation with source term ut=A(u)(uxxuyy-uxyuxy)+B(u)uxx+C(u)uyy+D(u)uxy+E(u), and obtained the exact solutions of the two equations when the parameters were determined.

Key words: parabolic MongeAmpère equation, exact solution, invariant set

CLC Number: 

  • O175.2