Linear Partial Differential Equations of First Order as Bi-Dimensional Inverse Moments Problem

Abstract

We consider linear partial differential equations of first order a(x,t)wx(x,t)+b(x,t)w1(x,t)=h(x,t)w(x,t)+r(x,t) on a region E=(a1, b1)x(a2,b2). We will see that we can write the equation in partial derivatives as an Fredholm integral equation of the first kind and will solve this latter with the techniques of inverse problem moments. We will find an approximated solution and bounds for the error of the estimated solution using the techniques on problem of moments.