We consider four definitions of solution to the initial-boundary value problem (IBVP) for a scalar balance laws in several space dimensions. These definitions are extended to the same most general framework and then compared. The first aim of this paper is to detail differences and analogies among them. We focus then on the ways the boundary conditions are fulfilled according to each definition, providing also connections among these various modes. The main result is the proof of the equivalence among the presented definitions of solution.

Definitions of solutions to the ibvp for multi-dimensional scalar balance laws / Rossi, Elena. - In: JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS. - ISSN 0219-8916. - 15:2(2018), pp. 349-374. [10.1142/S0219891618500133]

Definitions of solutions to the ibvp for multi-dimensional scalar balance laws

Rossi, Elena
2018

Abstract

We consider four definitions of solution to the initial-boundary value problem (IBVP) for a scalar balance laws in several space dimensions. These definitions are extended to the same most general framework and then compared. The first aim of this paper is to detail differences and analogies among them. We focus then on the ways the boundary conditions are fulfilled according to each definition, providing also connections among these various modes. The main result is the proof of the equivalence among the presented definitions of solution.
2018
15
2
349
374
Definitions of solutions to the ibvp for multi-dimensional scalar balance laws / Rossi, Elena. - In: JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS. - ISSN 0219-8916. - 15:2(2018), pp. 349-374. [10.1142/S0219891618500133]
Rossi, Elena
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1226955
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