### Session S08 - Inverse Problems and Applications

No date set.

## Solution of an integro-differential equation with conditions of Dirichlet using techniques of the inverse moments problem.

### María Beatriz Pintarelli

#### Universidad Nacional de La Plata, Argentina - This email address is being protected from spambots. You need JavaScript enabled to view it.

We want to find $w(x,t)$ such that
\[w_{t}= \int_{0}^{t}k(t-s)w_{xx}(x,s)ds+f(x,t)\]
about a domain $E= \left\lbrace (x,t),\quad 0

We will see that an approximate solution of the equation integro-differential can be found using the techniques of generalized inverse moments problem and bounds for the error of the estimated solution.

First the problem is reduced to solving a hyperbolic or parabolic partial derivative equation considering the unknown source. The method consists of two steps. In each one an integral equation is solved numerically using the two-dimensional inverse moments problem techniques. We illustrate the different cases with examples.