Global existence in 𝐿⁴(𝐑₊×𝐑) for a nonstrictly hyperbolic conservation law

Zhao, Huijiang

doi:10.1090/qam/1788422

Global existence in $L^4(\mathbf R_+\times \mathbf R)$ for a nonstrictly hyperbolic conservation law

Author: Huijiang Zhao
Journal: Quart. Appl. Math. 58 (2000), 627-660
MSC: Primary 35L65
DOI: https://doi.org/10.1090/qam/1788422
MathSciNet review: MR1788422
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Abstract: We study the existence problem for the following nonstrictly hyperbolic system: \[ {u_t} + \frac {1}{2}{\left ( 3{u^2} + {v^2} \right )_x} = 0\], \[ {v_t} + {\left ( uv \right )_x} = 0\], with singular initial data, i.e., \[ \left ( u\left ( t, x \right ), v\left ( t, x \right ) \right )\left | {_{t = 0}} \right . = \left ( {u_{0}}\left ( x \right ), {v_0}\left ( x \right ) \right ) \in {L^{4}}\left ( R, {R^{2}} \right )\].

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