%0 Journal Article
%T Global Solution of a Nonlinear Conservation Law with Weak Discontinuous Flux in the Half Space
%A Xiaoqian Li
%A Jing Zhang
%J American Journal of Computational Mathematics
%P 326-342
%@ 2161-1211
%D 2018
%I Scientific Research Publishing
%R 10.4236/ajcm.2018.84026
%X <div style=\"text-align:justify;\">
	<span style=\"font-family:Verdana;\">This paper is concerned with the initial-boundary value problem of a nonlinear conservation law in the half space <span style=\"font-family:Verdana;text-align:justify;white-space:normal;\"><i></i></span><i>R<span style=\"font-family:Verdana;text-align:justify;white-space:normal;\"></span></i></span><sup>+</sup>= {<span style=\"font-family:Verdana;text-align:justify;white-space:normal;\"><i></i></span><i>x </i>|<i><span style=\"font-family:Verdana;text-align:justify;white-space:normal;\"><i></i></span><i>x </i></i><span style=\"font-family:Verdana;text-align:justify;white-space:normal;\"></span>&gt; <span style=\"font-family:Verdana;text-align:justify;white-space:normal;\"></span>0}
</div>
<i><i><span style=\"font-family:Verdana;font-size:12px;\"> 
<div style=\"text-align:justify;\">
	<img src=\"Edit_0f72534e-e62a-4c6d-ba2d-ccc7b13e7538.png\" alt=\"\" /><br />
</div>
</span><span style=\"font-family:Verdana;font-size:12px;\"></span></i></i><span> 
<div style=\"text-align:justify;\">
	where<i> a&gt;0 , <i></i><i>u(<i></i><i>x,<i>t)</i></i></i></i> is an unknown function of <i><i><i><i> x ¡Ê R<sup>+</sup></i></i></i></i><i \"=\"\"><i></i></i> 
	<div style=\"display:inline !important;\">
		<i \"=\"\"><i><i><i><i><span style=\"white-space:nowrap;\"></span></i></i></i></i></i> 
		<div style=\"display:inline !important;\">
			<i \"=\"\"><i style=\"text-align:start;\"><i><i><i><i><span style=\"white-space:nowrap;\"></span></i></i></i></i></i></i> 
		</div>
	</div>
<span style=\"white-space:nowrap;\"></span>and<i><i><i><i> t&gt;0 , u<sub><span style=\"white-space:pre;\"> </span>¡À</sub> , <span style=\"white-space:nowrap;\">u<sub>m</sub></span> </i></i></i></i><span style=\"white-space:nowrap;\"></span><sub><span style=\"white-space:pre;\"></span></sub><span style=\"white-space:nowrap;\"><sub></sub></span>are three given constants satisfying <span style=\"white-space:nowrap;\"><em>u</em><sub>m</sub>=<em>u</em><sub>+</sub>¡Ù<em>u</em><sub>-</sub> </span> 
	<div style=\"display:inline !important;\">
		<i \"=\"\"><i><i><i><i> 
		<div style=\"display:inline !important;\">
			<i style=\"text-align:start;\"></i> 
		</div>
</i></i></i></i></i><i \"=\"\"><i></i></i> 
		<div style=\"display:inline !important;\">
			<i \"=\"\"></i> 
			<div style=\"display:inline !important;\">
				<i \"=\"\"><i><i><i><i><i></i></i></i></i></i></i> 
				<div style=\"display:inline !important;\">
					<i \"=\"\"><i></i></i> 
					<div style=\"display:inline !important;\">
						<i \"=\"\"><i><i
%K Nonlinear Conservation Laws with Weak Discontinuous Flux
%K Initial-Boundary Value Problem
%K Shock Wave
%K Rarefaction Wave
%K Contact Discontinuity
%K Interaction
%K Structure of Global Weak Entropy Solution
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=89633