An algebra of distributions and generalized solutions to nonlinear equations
In recent years, several works have considered generalized solutions to nonlinear differential equations. This problem eventually reduces to the multiplication of distributions. The known multiplication theory of Colombeau is convenient for proving existence theorems and using numerical methods, but it is not very constructive because the products of distributions are no longer functionals, which does not allow solutions to equations to be represented in an acceptable form. In this paper a method of finding generalized solutions to nonlinear equations, which is an analog of the method of undetermined coefficients for linear differential equations, is demonstrated.
generalized solutions to nonlinear differential equations
scientific article; zbMATH DE number 1037719