Consider the p-system describing the subsonic flow of a fluid in a pipe with section a = a(x). We prove that the resulting Cauchy problem generates a Lipschitz semigroup, provided the total variation of the initial datum and the oscillation of $a$ are small, while the total variation of $a$ needs to be suitably bounded. An explicit estimate on the bound of the total variation of a is provided, showing that at lower fluid speeds, higher total variations of a are acceptable. An example shows that the bound on TV(a) is mandatory, for otherwise the total variation of the solution may grow arbitrarily
Colombo, R.M., & Marcellini, F. (2010). Smooth and discontinuous junctions in the p-system. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 361(2), 440-456.
Citazione: | Colombo, R.M., & Marcellini, F. (2010). Smooth and discontinuous junctions in the p-system. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 361(2), 440-456. |
Tipo: | Articolo in rivista - Articolo scientifico |
Carattere della pubblicazione: | Scientifica |
Titolo: | Smooth and discontinuous junctions in the p-system |
Autori: | Colombo, RM; Marcellini, F |
Autori: | |
Data di pubblicazione: | 2010 |
Lingua: | English |
Rivista: | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/j.jmaa.2009.07.022 |
Appare nelle tipologie: | 01 - Articolo su rivista |