Resumen de A Hamiltonian Regularization of the Burgers Equation

H. S. Bhat, R. C. Fetecau

• We consider a quasilinear equation that consists of the inviscid Burgers equation plus O(?2) nonlinear terms. As we show, these extra terms regularize the Burgers equation in the following sense: for smooth initial data, the ? > 0 equation has classical solutions globally in time. Furthermore, in the zero-? limit, solutions of the regularized equation converge strongly to weak solutions of the Burgers equation. We present numerical evidence that the zero-? limit satisfies the Oleinik entropy inequality. For all ? ? 0, the regularized equation possesses a nonlocal Poisson structure. We prove the Jacobi identity for this generalized Hamiltonian structure.