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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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.
|Uncontrolled Keywords:||Conservation law; Nonhomogeneous boundary conditions; Continuous flux; Penalization; L1-Theory;Renormalized entropy solution|
|Subjects:||Sciences > Mathematics > Differential equations|
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|Deposited On:||11 Jun 2012 10:06|
|Last Modified:||18 Apr 2013 16:32|
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