TY - JOUR
T1 - On renormalized dissipative solutions for conservation laws
AU - Takagi, Satoru
PY - 2005/11/30
Y1 - 2005/11/30
N2 - We introduce a new notion of renormalized dissipative solutions for a scalar conservation law ut+divF(u)=f with locally Lipschitz F and L1 data, and prove the equivalence of such solutions and renormalized entropy solutions in the sense of Bénilan et al. The structure of renormalized dissipative solutions is useful to deal with relaxation systems than the renormalized entropy scheme. As an application of our result, we prove the existence of renormalized dissipative solutions via relaxation.
AB - We introduce a new notion of renormalized dissipative solutions for a scalar conservation law ut+divF(u)=f with locally Lipschitz F and L1 data, and prove the equivalence of such solutions and renormalized entropy solutions in the sense of Bénilan et al. The structure of renormalized dissipative solutions is useful to deal with relaxation systems than the renormalized entropy scheme. As an application of our result, we prove the existence of renormalized dissipative solutions via relaxation.
KW - Conservation laws
KW - Locally Lipschitz continuous
KW - Renormalized dissipative solutions
KW - Renormalized entropy solutions
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U2 - 10.1016/j.na.2005.03.002
DO - 10.1016/j.na.2005.03.002
M3 - Article
AN - SCOPUS:28044458961
SN - 0362-546X
VL - 63
SP - e2483-e2489
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
IS - 5-7
ER -