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The Initial and Neumann Boundary Value Problem for a Class Parabolic Monge-Ampère Equation

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  • Juan Wang
  • Jinlin Yang
  • Xinzhi Liu

Abstract

We consider the existence, uniqueness, and asymptotic behavior of a classical solution to the initial and Neumann boundary value problem for a class nonlinear parabolic equation of Monge-Ampère type. We show that such solution exists for all times and is unique. It converges eventually to a solution that satisfies a Neumann type problem for nonlinear elliptic equation of Monge-Ampère type.

Suggested Citation

  • Juan Wang & Jinlin Yang & Xinzhi Liu, 2013. "The Initial and Neumann Boundary Value Problem for a Class Parabolic Monge-Ampère Equation," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, July.
    • Handle: RePEc:hin:jnlaaa:535629
    DOI: 10.1155/2013/535629
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    Cited by:

    1. Andrei D. Polyanin & Alexander V. Aksenov, 2024. "Unsteady Magnetohydrodynamics PDE of Monge–Ampère Type: Symmetries, Closed-Form Solutions, and Reductions," Mathematics, MDPI, vol. 12(13), pages 1-29, July.

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