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GLOBAL EXISTENCE IN L⁴(R₊ × R) FOR A NONSTRICTLY HYPERBOLIC CONSERVATION LAW

HUIJIANG ZHAO
Quarterly of Applied Mathematics
Vol. 58, No. 4 (December 2000), pp. 627-660
Published by: Brown University
Stable URL: http://www.jstor.org/stable/43638504
Page Count: 34
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
GLOBAL EXISTENCE IN L⁴(R₊ × R) FOR A NONSTRICTLY HYPERBOLIC CONSERVATION LAW
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Abstract

We study the existence problem for the following nonstrictly hyperbolic system: ${u_t}\, + \,\frac{1}{2}(3{u^2}\, + \,{\upsilon ^2})x\, = 0,$ vt + (uv)x = 0, with singular initial data, i. e., (u(t, x), v(t, x))|t=0 = (u₀(x), v₀(x)) ∈ L⁴(R, R²). A strong convergence result of the L⁴(R₊ × R, R²) bounded approximating sequences generated by the method of vanishing viscosity is obtained. The analysis uses Young measure, half-plane-supported entropy-entropy flux pairs, and Tartar-Murat's theory of compensated compactness.

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