# Nonlinear PDE with convolution

I would like to find a numeric solution to the following nonlinear evolution equation (a.k.a. PDE) $$\frac{\partial }{\partial t} u(t,x)=f\left(u(t,x),\int_{-\infty}^\infty a(x-y)u(t,y)dy\right),$$ where $a$ is an integrable function, say, $a(x)=e^{-x^2}$ and $f$ is a "good" function, e.g. $f(p,q)=q-pe^{-q}$. Is it possible to do this with Mathematica?

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Can you supply the boundary conditions.. –  PlatoManiac Jun 21 at 11:31
This is an evolution equation, so, I have an initial value problem, say, $u(0,x)=\frac{1}{1+x^2}$, $x\in \mathbb{R}$. But without any bounded domain for $x\in\mathbb{R}$. –  Dmitri Jun 21 at 11:53
You would want to use NDSolve for that, however "Delay partial differential equations are not currently supported by NDSolve". –  b.gatessucks Jun 22 at 8:11