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.
|ジャーナル||Nonlinear Analysis, Theory, Methods and Applications|
|出版ステータス||Published - 2005 11月 30|
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