Non linear second order partial differential equations as generalized inverse moment problems

Abstract

General forms for non linear elliptic, hyperbolic and parabolic partial differential equations are considered. For all these we present a general procedure that transforms they into a Fredholm integral equation of the first kind. The resulting integral equations are then handled as a generalized moment problem. An inversion algorithm as well as conditions for the stability for the solution of this last are given. Some examples show the accuracy of the inversion method.