Non-standard parabolic regularization of the gradient catastrophes for the Burgers-Hopf equation is proposed. It is based on the analysis of all (generic and higher order) gradient catastrophes and their step-by-step regularization by embedding the Burgers-Hopf equation into the multi-component parabolic systems of the quasilinear PDEs with the most degenerate Jordan block. The probabilistic realization of such a procedure is presented. The complete regularization of the Burgers-Hopf equation is achieved by embedding it into an infinite parabolic Jordan chain. It is shown that the Burgers equation is a particular reduction of the Jordan chain. Gradient catastrophes for the parabolic Jordan systems are also studied.

Konopelchenko, B., Ortenzi, G. (2018). Parabolic regularization of the gradient catastrophes for the Burgers-Hopf equation and Jordan chain. JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL, 51(27), 1-27 [10.1088/1751-8121/aac544].

Parabolic regularization of the gradient catastrophes for the Burgers-Hopf equation and Jordan chain

Ortenzi, G
2018

Abstract

Non-standard parabolic regularization of the gradient catastrophes for the Burgers-Hopf equation is proposed. It is based on the analysis of all (generic and higher order) gradient catastrophes and their step-by-step regularization by embedding the Burgers-Hopf equation into the multi-component parabolic systems of the quasilinear PDEs with the most degenerate Jordan block. The probabilistic realization of such a procedure is presented. The complete regularization of the Burgers-Hopf equation is achieved by embedding it into an infinite parabolic Jordan chain. It is shown that the Burgers equation is a particular reduction of the Jordan chain. Gradient catastrophes for the parabolic Jordan systems are also studied.
Articolo in rivista - Articolo scientifico
Jordan chain; non-generic gradient catastrophes; parabolic regularization; Statistical and Nonlinear Physics; Statistics and Probability; Modeling and Simulation; Mathematical Physics; Physics and Astronomy (all)
English
2018
1
27
27
Konopelchenko, B., Ortenzi, G. (2018). Parabolic regularization of the gradient catastrophes for the Burgers-Hopf equation and Jordan chain. JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL, 51(27), 1-27 [10.1088/1751-8121/aac544].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/211160
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