1. Aug 6, 2010

### mnourian

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.

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

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