Decay of solutions for the equations of isothermal gas dynamics

Wave-front tracking for the equations of isentropic gas dynamics

“…10 and also Asakura [2]). We can also verify that our solutions fulfill all requirements of Theorem 5.7 in Liu [9], which implies If we assume further that there is a constant M > 0 such that the initial value satisfies U 0 (x) = U ∞ for |x| ≥ M , then the argument in Asakura [1] shows that T.V.U ( * , t) approaches zero at the rate t −1/2 .…”

“…A single shock front is a part of a finite number of paths and the strength of the shock front is the summation of the strength of these paths. The notion of the path has been introduced by Temple-Young [15] and the idea of this decomposition has already been used in this author's previous paper [1]. In sections 2, 3 and 4, we will summarise basic results on the Riemann problem, the wave-front tracking scheme following [4], and the interaction estimates obtained by [11].…”

“…We define a (2, 1)-segment γ (1) and (2, 2)-segment γ (2) so that |γ (2) | = δ 2 ζ and |γ | = |γ (1) | + |γ (2) |. Thus Γ is divided into two paths and extended beyond P 1 such that…”

Asymptotic stability of solutions with strong discontinuities for the equations of isothermal gas dynamics

“…This note is a continuation of previous works [1], [2] and [3]. We study the Cauchy problem for a hyperbolic system of conservation laws of the form:…”

“…The decisive part of his proof consists in showing that the negative variation in x of a Glimm approximate solution does not increase as t passes. In [1], we further studied the interaction of simple waves and Showed that the total amount of interaction of simplc waves in the Nishida solution is boundcd provided the total variation of initial data is finite: In particular, we have…”