We investigate the properties of the set of singularities of semiconcave solutions of Hamilton-Jacobi equations. It is well known that the singularities of such solutions propagate locally along generalized characteristics. Special generalized characteristics, satisfying an energy condition, can be constructed, under some assumptions on the structure of the Hamiltonian H. In this paper, we provide estimates of the dissipative behavior of the energy along such curves. As an application, we prove that the singularities of any viscosity solution of such equations cannot vanish in a finite time.

Cannarsa, P., Mazzola, M., Sinestrari, C. (2015). Global Propagation of Singularities for Time Dependent Hamilton-Jacobi Equations. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 38, 441-469 [10.3934/dcds.2015.35.4225].

Global Propagation of Singularities for Time Dependent Hamilton-Jacobi Equations

CANNARSA, PIERMARCO;SINESTRARI, CARLO
2015-01-01

Abstract

We investigate the properties of the set of singularities of semiconcave solutions of Hamilton-Jacobi equations. It is well known that the singularities of such solutions propagate locally along generalized characteristics. Special generalized characteristics, satisfying an energy condition, can be constructed, under some assumptions on the structure of the Hamiltonian H. In this paper, we provide estimates of the dissipative behavior of the energy along such curves. As an application, we prove that the singularities of any viscosity solution of such equations cannot vanish in a finite time.
2015
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/05 - ANALISI MATEMATICA
English
Con Impact Factor ISI
This work was co-funded by the European Union under the 7th Framework Programme “FP7-PEOPLE-2010-ITN”, grant agreement number 264735-SADCO, by the INdAM national group GNAMPA and the INdAM-CNRS GDRE CONEDP.
Cannarsa, P., Mazzola, M., Sinestrari, C. (2015). Global Propagation of Singularities for Time Dependent Hamilton-Jacobi Equations. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 38, 441-469 [10.3934/dcds.2015.35.4225].
Cannarsa, P; Mazzola, M; Sinestrari, C
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/113950
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