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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.

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# How to solve this nonlinear PDE? Please help

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