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

J.-A. Marti

Vol. 210 (2003), No. 1, 165–187

DOI: 10.2140/pjm.2003.210.165

Abstract

By means of three fundamental structures we can define, 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 δ-Dirac measure as initial data, and we can construct a generalized δ-shock wave as an approximate solution, self-similar to the initial data.

Milestones

Received: 30 June 1999

Published: 1 May 2003