An explicit lower bound of viscosity solutions to isentropic gas dynamics and Euler equation

The main contribution of this paper is to use the maximum principle to obtain the explicit lower bound of #rho#"#epsilon# #>=# C(t, #epsilon#) > 0 for the parabolic system generated by adding 'artificial viscosity' to the systems of one-dimensional isentropic gas dynamics and to the Euler equation corresponding to the Broadwell model, where C(t,#epsilon#) are given respectively. Here we don't need the restriction (#rho#_0(#+-##infinity#), u_0(#+-##infinity#)) = (anti #rho#, anti u). As a by-product, we get the existence of the generalized solution for the systems of the isentropic, polytropic gas dynamics with bounded measurable initial data (#rho#0(x), u_0(x)), (#rho#_0(x) #>=# 0) when the adiabatic exponent #gamma# element of (1, 5/3) by using the framework. (orig.)SIGLEAvailable from TIB Hannover: RR 1606(95-18) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

The Cauchy problem for hyperbolic conservation laws with three equations

SIGLEAvailable from TIB Hannover: RR 1606(95-16) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

The Cauchy problem for hyperbolic conservation laws with three equations

SIGLEAvailable from TIB Hannover: RR 1606(95-16) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman