# Volterra equations

1. Oct 2, 2011

### alecrimi

Hi Guys!
I have a (stupid) question. In which physical phenomena do you use Volterra equations (or similar equations) ?
I mean if we go back to traditional heat,diffusion,wave, transport... and so on we know more or less when to use them. Are integral equation just a dual representation or is there a specific reason to use them ?
Thanx
Alex

2. Oct 2, 2011

### Dickfore

A differential equation:

$$y' = f(x, y)$$

with the initial condition $y(x_{0}) = y_{0}$ is equivalent to the integral equation:

$$y(x) = y_{0} + \int_{x_{0}}^{x}{f(t, y(t)) \, dt}$$

This is a Volterra (since the upper bound of the integral is variable) integral equation of the second kind (since the unknown function $y(x)$ is both under the integral and outside).

3. Oct 2, 2011

### alecrimi

Probably my question was not clear. I didn't ask for a definition (everybody can look up wikipedia), I asked when do you need to use them ?
some inverse problem... for example ? I am asking when did you meet them, in which phenomena ?

Last edited: Oct 2, 2011
4. Oct 2, 2011

### Dickfore

Is what I typed a definition?