Nonlinear algebraic analysis of delta shock wave solutions to Burgers' equation

By means of three fundamental structures we can de. ne, in a general way, a sheaf A of differential algebras containing most of the special cases met in the theory of generalized functions. A convenient choice of these structures permits us to study Burgers' equation with delta-Dirac measure as initial data, and we can construct a generalized delta-shock wave as an approximate solution, self-similar to the initial data.