# nonlinear partial differential equation

I'm considering the following type of PDE: $u_t=\frac{u_{xx}+u_{x}}{u_t^2}$. Are there any currents methods for studying the well posedness of such an equation at zero. (I don't have much of a background in PDE's sorry in advance if my question is ill posed)

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Is there any reason why you don't write it as $u_t^3 = u_{xx} + u_x$? – Christopher A. Wong Oct 12 '12 at 10:14