Differential and Integral Equations

On a degenerate scalar conservation law with general boundary condition

Kaouther Ammar and Petra Wittbold

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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 $a\in L^\infty(\Sigma).$

Article information

Differential Integral Equations, Volume 21, Number 3-4 (2008), 363-386.

First available in Project Euclid: 20 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35L65: Conservation laws
Secondary: 35D30: Weak solutions 35F30: Boundary value problems for nonlinear first-order equations


Ammar, Kaouther; Wittbold, Petra. On a degenerate scalar conservation law with general boundary condition. Differential Integral Equations 21 (2008), no. 3-4, 363--386. https://projecteuclid.org/euclid.die/1356038785

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