An equivalent definition of renormalized entropy solutions for scalar conservation laws
An equivalent definition of renormalized entropy solutions for scalar conservation laws
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 …