A Hamiltonian Regularization of the Burgers Equation

• Autores: H. S. Bhat, R. C. Fetecau
• Localización: Journal of nonlinear science, ISSN 0938-8974, Vol. 16, Nº 6, 2006, págs. 615-638
• Idioma: inglés
• DOI: 10.1007/s00332-005-0712-7
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• Resumen

  • 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.