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

### María Beatriz Pintarelli

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 $E= \left\lbrace (x,t),\quad 00 \right\rbrace$, with conditions $w(x,0)=h_{1}(x); \qquad w(0,t)=k_{1}(t); \qquad w(L,t)=k_{2}(t)$ where $k(x)$ has continuous derivative on $x=0$, the value of $k(0)$ is known, $f(x,t)$ known and derivative with respect to $t$ continuous, using the problem generalized moments techniques.