Let H be a bounded and Lipschitz continuous function. We consider discontinuous viscosity solutions of the Hamilton–Jacobi equation Ut+ H(Ux) = 0 and signed Radon measure valued entropy solutions of the conservation law ut+ [H(u)] x= 0. After having proved a precise statement of the formal relation Ux= u, we establish estimates for the (strictly positive!) times at which singularities of the solutions disappear. Here singularities are jump discontinuities in case of the Hamilton–Jacobi equation and signed singular measures in case of the conservation law.

Bertsch, M., Smarrazzo, F., Terracina, A., Tesei, A. (2021). Discontinuous solutions of Hamilton–Jacobi equations versus Radon measure-valued solutions of scalar conservation laws: disappearance of singularities. JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS [10.1007/s10884-021-09997-x].

Discontinuous solutions of Hamilton–Jacobi equations versus Radon measure-valued solutions of scalar conservation laws: disappearance of singularities

Bertsch M.;
2021

Abstract

Let H be a bounded and Lipschitz continuous function. We consider discontinuous viscosity solutions of the Hamilton–Jacobi equation Ut+ H(Ux) = 0 and signed Radon measure valued entropy solutions of the conservation law ut+ [H(u)] x= 0. After having proved a precise statement of the formal relation Ux= u, we establish estimates for the (strictly positive!) times at which singularities of the solutions disappear. Here singularities are jump discontinuities in case of the Hamilton–Jacobi equation and signed singular measures in case of the conservation law.
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/05
English
First order hyperbolic conservation laws
Hamilton–Jacobi equation
Singular boundary conditions
Waiting time
Bertsch, M., Smarrazzo, F., Terracina, A., Tesei, A. (2021). Discontinuous solutions of Hamilton–Jacobi equations versus Radon measure-valued solutions of scalar conservation laws: disappearance of singularities. JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS [10.1007/s10884-021-09997-x].
Bertsch, M; Smarrazzo, F; Terracina, A; Tesei, A
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2108/304339
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