The initial-boundary value problem for a general balance law in a bounded domain is proved to be well posed. Indeed, we show the existence of an entropy solution, its uniqueness and its Lipschitz continuity as a function of time, of the initial datum and of the boundary datum. The proof follows the general lines in [4], striving to provide a rigorous treatment and detailed references.
Rigorous estimates on balance laws in bounded domains / Colombo, Rm; Rossi, Elena. - In: ACTA MATHEMATICA SCIENTIA. - ISSN 0252-9602. - 35:4(2015), pp. 906-944. [10.1016/S0252-9602(15)30028-X]
Rigorous estimates on balance laws in bounded domains
ROSSI, ELENA
2015
Abstract
The initial-boundary value problem for a general balance law in a bounded domain is proved to be well posed. Indeed, we show the existence of an entropy solution, its uniqueness and its Lipschitz continuity as a function of time, of the initial datum and of the boundary datum. The proof follows the general lines in [4], striving to provide a rigorous treatment and detailed references.
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