Solution of a system of differential equations with constant coefficients using in-verse moments problem techniques

It is known that given a system of simultaneous linear differential equations with constant coefficients you can apply the Laplace method to solve it. The Laplace transforms are found and the problem is reduced to the resolution of an algebraic system of equations of the determining functions, and applying the inverse transformation the generating functions are determined, solutions of the given system. This implies the need to know the analytical form of the inverse transform of the function. In this case the initial conditions consist in knowing the value that the generating function and its derivatives takes at zero. A generalization of this method is proposed in this work, which is to define a more general integral operator than the Laplace transform, the initial conditions consist of Cauchy conditions in the contour. And finally, we find a numerical approximation of the inverse transformation of the generating functions, using the techniques of inverse moment problems, without being necessary to know the analytical form of the inverse transform of the function.

A problem of coefficient determination in parabolic equations solved as moment problem

The problem is to find a(t) y w(x; t) such that wt = a(t) (wx)x+r(x; t) under the initial condition w(x; 0) =fi(x) and the boundary conditions w(0; t) = 0 ; wx(0; t) = wx(1; t)+alfa w(1; t) about a region D ={(x; t); 0 <x < 1; t >0}. In addition it must be fulfilled the integral of w (x, t) with respect to x is equal to E(t) where fi(x) , r(x; t) and E(t) are known functions and alfa is an arbitrary real number other than zero.The objective is to solve the problem as an application of the inverse moment problem. We will find an approximated solution and bounds for the error of the estimated solution using the techniques on moments problem. In addition, the method is illustrated with several examples.