We consider a hyperbolic system of two conservation laws, in one space dimension, modelling phase transitions; these are understood as discontinuous solutions with values in two disjoint open sets of the state space. For states close to a subsonic phase transition the Riemann problem is underdetermined, and we select the phase boundary by an entropy equality. In the limit sonic case, we still use such a criterion either for subsonic and sonic phase boundaries; some conditions are needed to solve the Riemann problems. These assumptions are satisfied by some significant models if the phase boundary is chosen according to a viscosity-capillarity criterion. In both cases we provide results of global existence of solutions to the Cauchy problem if the initial data have suitable small total variation.
Subsonic and sonic phase transitions
CORLI, Andrea
2000
Abstract
We consider a hyperbolic system of two conservation laws, in one space dimension, modelling phase transitions; these are understood as discontinuous solutions with values in two disjoint open sets of the state space. For states close to a subsonic phase transition the Riemann problem is underdetermined, and we select the phase boundary by an entropy equality. In the limit sonic case, we still use such a criterion either for subsonic and sonic phase boundaries; some conditions are needed to solve the Riemann problems. These assumptions are satisfied by some significant models if the phase boundary is chosen according to a viscosity-capillarity criterion. In both cases we provide results of global existence of solutions to the Cauchy problem if the initial data have suitable small total variation.I documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
