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Strong traces for solutions of multidimensional scalar conservation laws. (English) Zbl 0999.35018
Author’s abstract: In this paper we consider multidimensional scalar conservation laws without BV estimates defined in a subset \(\Omega \subset \mathbb{R}^+ \times \mathbb{R}^d\). We show that, with a nonlinear degeneracy hypothesis on the flux, we can define a strong notion of trace at the boundary of \(\Omega\) reached by \(L^1\) convergence.
Reviewer: E.Feireisl (Praha)

MSC:
35D10 Regularity of generalized solutions of PDE (MSC2000)
35L65 Hyperbolic conservation laws
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
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