Abstract
We introduce a new notion of renormalized dissipative solutions for a scalar conservation law $u_{t}+\mathrm{div}\, {\mathrm{\mathbf{F}}}(u)=f$ with locally Lipschitz ${\mathrm{\mathbf{F}}}$ and $L^{1}$ data, and prove the equivalence of such solutions and renormalized entropy solutions in the sense of Benilan et al. The structure of renormalized dissipative solutions is more useful in dealing with relaxation systems than the renormalized entropy scheme. As an example, we apply our result to contractive relaxation systems in merely an $L^{1}$ setting and construct a renormalized dissipative solution via relaxation.
Citation
Kazuo Kobayasi. Satoru Takagi. "An equivalent definition of renormalized entropy solutions for scalar conservation laws." Differential Integral Equations 18 (1) 19 - 33, 2005. https://doi.org/10.57262/die/1356060234
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