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2008 On a degenerate scalar conservation law with general boundary condition
Kaouther Ammar, Petra Wittbold
Differential Integral Equations 21(3-4): 363-386 (2008). DOI: 10.57262/die/1356038785


We study a degenerate scalar conservation law on a bounded domain with non homogeneous boundary condition: $b(v)_t + \mbox{div } \Phi(v)=f $ on $Q:= (0,T) \times \Omega$, $v(0,\cdot)=v_0$ on $\Omega$ and $v=a$ on the boundary $(0,T) \times \partial \Omega$. The function $b$ is assumed to be continuous nondecreasing and to verify the normalization condition $b(0)=0.$ Existence and uniqueness of a renormalized entropy solution is established for any $\Phi \in C({{\mathbb R}};{{\mathbb R}}^N)$, $v_0\in L^\infty(\Omega)$, $f \in L^\infty(Q)$, and boundary data $a\in L^\infty(\Sigma).$


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Kaouther Ammar. Petra Wittbold. "On a degenerate scalar conservation law with general boundary condition." Differential Integral Equations 21 (3-4) 363 - 386, 2008.


Published: 2008
First available in Project Euclid: 20 December 2012

zbMATH: 1224.35061
MathSciNet: MR2484014
Digital Object Identifier: 10.57262/die/1356038785

Primary: 35L65
Secondary: 35D30 , 35F30

Rights: Copyright © 2008 Khayyam Publishing, Inc.

Vol.21 • No. 3-4 • 2008
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