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
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 |
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| Deposited On: | 11 Jun 2012 10:06 |
| Last Modified: | 18 Apr 2013 16:32 |
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