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Scalar conservation laws with general boundary condition and continuous flux function.

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Ammar, Kaouther and Wittbold, Petra and Carrillo Menéndez, José (2006) Scalar conservation laws with general boundary condition and continuous flux function. Journal of Differential Equations, 228 (1). pp. 111-139. ISSN 0022-0396

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Official URL: http://www.sciencedirect.com/science/article/pii/S002203960600204X


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Abstract

We introduce a notion of entropy solution for a scalar conservation law on a bounded domain with nonhomogeneous boundary condition: u(t) + div Phi (u) = f on Q = (0, T) x Omega, u (0, (.))= u(0) on Q and "u = a on some part of the boundary (0, T) x partial derivative Omega." Existence and uniqueness of the entropy solution is established for any Phi is an element of C(R; R-N), u(0) is an element of L-infinity(Q), f is an element of L-infinity(Q), a is an element of L-infinity((0, T) x partial derivative Omega). In the L-1-setting, a corresponding result is proved for the more general notion of renormalised entropy solution.


Item Type:Article
Uncontrolled Keywords:Conservation law; Nonhomogeneous boundary conditions; Continuous flux; Penalization; L1-Theory;Renormalized entropy solution
Subjects:Sciences > Mathematics > Differential equations
ID Code:15555
Deposited On:11 Jun 2012 08:06
Last Modified:12 Dec 2018 15:07

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