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. 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., Marcellini, F. (2010). Smooth and discontinuous junctions in the p-system. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 361(2), 440-456 [10.1016/j.jmaa.2009.07.022].
Smooth and discontinuous junctions in the p-system
MARCELLINI, FRANCESCA
2010
Abstract
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. 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.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
