Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



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:

$\displaystyle {u_t} + \frac{1}{2}{\left( 3{u^2} + {v^2} \right)_x} = 0$


$\displaystyle {v_t} + {\left( uv \right)_x} = 0$

, with singular initial data, i.e.,

$\displaystyle \left( u\left( t, x \right), v\left( t, x \right) \right)\left\ve... ...( x \right), {v_0}\left( x \right) \right) \in {L^{4}}\left( R, {R^{2}} \right)$


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DOI: https://doi.org/10.1090/qam/1788422
Article copyright: © Copyright 2000 American Mathematical Society

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