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How to solve this nonlinear PDE? Please help

  1. Aug 6, 2010 #1
    How to solve this nonlinear PDE??? Please help!!

    Hello Everyone,

    I am trying to solve the following nonlinear PDE which is driven from the Hamilton Jacobi Bellman (HJB) equation in ergodic control of a nonlinear dynamical system.

    [tex]v\nabla_x h - \frac{1}{4}\|\nabla_v h\|^2 + \frac{1}{2} \sigma \Delta h + m(x,v) = \rho [/tex].

    Please note that:

    1-[tex] h(x,v)[/tex] is a function of [tex]x[/tex] (position) and [tex]v[/tex] velocity.
    2-[tex]m(x,v)[/tex] is a function of [tex]x,v[/tex] (can be assumed to be seperabale)
    3- [tex]\rho[/tex] is a constant
    4- [tex]\nabla[/tex] is the gradient operator.
    5- [tex]\Delta[/tex] is the Laplacian operator.

    I do not even know what kind of equation I have (in the PDE word)?

    I would really appreciate it if you could help me.

    Many thanks.
    Last edited: Aug 6, 2010
  2. jcsd
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