In:
Abstract and Applied Analysis, Hindawi Limited, Vol. 2014 ( 2014), p. 1-7
Kurzfassung:
We obtain the global existence of weak solutions for the Cauchy problem of the nonhomogeneous, resonant system. First, by using the technique given in Tsuge (2006), we obtain the uniformly bounded L ∞ estimates z ( ρ δ , ε , u δ , ε ) ≤ B ( x ) and w ( ρ δ , ε , u δ , ε ) ≤ β when a ( x ) is increasing (similarly, w ( ρ δ , ε , u δ , ε ) ≤ B ( x ) and z ( ρ δ , ε , u δ , ε ) ≤ β when a ( x ) is decreasing) for the ε -viscosity and δ -flux approximation solutions of nonhomogeneous, resonant system without the restriction z 0 ( x ) ≤ 0 or w 0 ( x ) ≤ 0 as given in Klingenberg and Lu (1997), where z and w are Riemann invariants of nonhomogeneous, resonant system; B ( x ) 〉 0 is a uniformly bounded function of x depending only on the function a ( x ) given in nonhomogeneous, resonant system, and β is the bound of B ( x ) . Second, we use the compensated compactness theory, Murat (1978) and Tartar (1979), to prove the convergence of the approximation solutions.
Materialart:
Online-Ressource
ISSN:
1085-3375
,
1687-0409
Sprache:
Englisch
Verlag:
Hindawi Limited
Publikationsdatum:
2014
ZDB Id:
2064801-7
SSG:
17,1
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