On the Hamilton–Jacobi equation in the framework of generalized functions

In this work we study, in the framework of Colombeauʼs generalized functions, the Hamilton–Jacobi equation with a given initial condition. We have obtained theorems on existence of solutions and in some cases uniqueness. Our technique is adapted from the classical method of characteristics with a wide use of generalized functions. We were led also to obtain some general results on invertibility and also on ordinary differential equations of such generalized functions.