This paper is concerned with systems of 2 x 2 conservation laws (star) partial derivative(t)u + partial derivative(x) [f(u)] = 0, t greater than or equal to 0, x is an element of R, u is an element of R-2, developing phase transitions, as happens in models related to elastodynamics or to van der Waals fluids, for instance. In the present paper, a definition of Psi-admissible solution to (star) is given which comprises the various definitions in the current literature. Furthermore, the Psi-admissible Riemann semigroup (Psi RS) generated by (star) is introduced and constructed by means of a wave-front tracking algorithm. Uniqueness and continuous dependence for Psi-admissible solutions to (star) thus follow.
Continuous dependence in conservation laws with phase transitions
CORLI, Andrea
1999
Abstract
This paper is concerned with systems of 2 x 2 conservation laws (star) partial derivative(t)u + partial derivative(x) [f(u)] = 0, t greater than or equal to 0, x is an element of R, u is an element of R-2, developing phase transitions, as happens in models related to elastodynamics or to van der Waals fluids, for instance. In the present paper, a definition of Psi-admissible solution to (star) is given which comprises the various definitions in the current literature. Furthermore, the Psi-admissible Riemann semigroup (Psi RS) generated by (star) is introduced and constructed by means of a wave-front tracking algorithm. Uniqueness and continuous dependence for Psi-admissible solutions to (star) thus follow.I documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
