Parabolic Partial Differential Equations with Border Conditions of Dirichlet as Inverse Moments Problem

Abstract

We considerer parabolic partial differential equations. We will see that an approximate solution can be found using the techniques of generalized inverse moments problem and also bounds for the error of estimated solution. First we transform the parabolic partial differential equation to the integral equation. Using the inverse moments problem techniques we obtain an approximate solution. Then we find a numerical approximation of when solving the integral equation, because solving the previous integral equation is equivalent to solving the equation