Solutions in the large for some nonlinear hyperbolic conservation laws

✍ Scribed by Takaaki Nishida; Joel A. Smoller

• Publisher: John Wiley and Sons
• Year: 1973
• Tongue: English
• Weight: 513 KB
• Volume: 26
• Category: Article
• ISSN: 0010-3640
• DOI: 10.1002/cpa.3160260205

✦ Synopsis

Here u is the specific volume, u = I/p, p is the density and u is the speed of the gas. The equation of state of the gas is p ( v ) = k2/uY, where y is a constant, y = 1 + 2 ~, and E will be a small positive constant throughout this paper.

We consider the initial value problem for (1) in the region t 2 0, x E R, with initial values and assume that vo(x) and uo(x) are bounded and have bounded total variation. We further assume that there are constants 41, fi such that

X E R .

Under these assumptions we shall prove that the initial value problem ( l ) ,

(2) has a (weak) solution defined for all time, provided that (3) Etotal var. {uo(x), u o ( x ) } * The first author was supported by an IBM postdoctoral fellowship and a Sloan Foundation postdoctoral fellowship at the