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.
Colombo, R., Rossi, E. (2015). Rigorous estimates on balance laws in bounded domains. ACTA MATHEMATICA SCIENTIA, 35(4), 906-944 [10.1016/S0252-9602(15)30028-X].
Rigorous estimates on balance laws in bounded domains
ROSSI, ELENAUltimo
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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