Generalizing the Bardos-LeRoux-Nédélec boundary condition for ...

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The problem BLN condition & Alternatives Effective BC graph Definition Uniqueness Definition Bis Existence & Convergence of Approximations ...Alternatives to BLN approach, boundary traces... (A. Vasseur (’01), E.Yu. Panov (’07)) revival of the original BLN strong-trace formulation: the strong trace of a merely L ∞ entropy solution u does exist !!! (a bit less than this, but still sufficient for our needs...) This subtle “regularity” result for entropy solutions comes along with compactifying effects of the non-linearity ϕ (P.L. Lions, B. Perthame, and E. Tadmor (’94), E.Yu. Panov (’94)).
The problem BLN condition & Alternatives Effective BC graph Definition Uniqueness Definition Bis Existence & Convergence of Approximations ...Alternatives to BLN approach, boundary traces... (A. Vasseur (’01), E.Yu. Panov (’07)) revival of the original BLN strong-trace formulation: the strong trace of a merely L ∞ entropy solution u does exist !!! (a bit less than this, but still sufficient for our needs...) This subtle “regularity” result for entropy solutions comes along with compactifying effects of the non-linearity ϕ (P.L. Lions, B. Perthame, and E. Tadmor (’94), E.Yu. Panov (’94)). To state the Panov’s result, let us give the following definition. Definition A function u ∈ L ∞ ((0, T ) × Ω) is called quasi-solution for the operator ut + div ϕ(u) if ∀k ∈ R η ± k (u)t + div q ± k (u) = −µ± k in D′ ((0, T ) × Ω), where (η ± k , q± k ) are the Kruzhkov entropy-flux pairs and µ± k are Borel measures on (0, T ) × Ω, finite up to the boundary .
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Generalizing the Bardos-LeRoux-Nédélec boundary condition for ...

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