Hello,

I am wondering whether it is possible to convert the following integral equation to a partial differential equation.

Integral Equation here http://ima.epfl.ch/~lechen/images/integralEq.jpg

where $J_0(t,x)$ is some given nonnegative function and $\nu>0$ is a constant. It is clear $t\ge 0$.

The aim is to solve this equation. To convert it to PDE is just one possible way to solve it, since latter we can use the hopefully the fundamental solutions.

My current solution is

PDE http://ima.epfl.ch/~lechen/images/PDE.jpg

But I am not sure whether it is right or not.

Thanks for any comments or hints!