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

The problem BLN condition & Alternatives Effective BC graph Definition Uniqueness Definition Bis Existence & Convergence of Approximations
The BLN condition and its extrapolation.
Our goal is to generalize condition (BLN) by replacing β = {0} × R
with a general maximal monotone graph.
Let us first reformulate the boundary condition as :
(γu, γϕν(u)) ∈ β (t,x)
( i.e., ϕν(γu) ∈ β (t,x)(u) ),
where β (t,x) is the following maximal monotone subgraph of ϕν(.):
(Dubois,LeFloch ):
β (t,x) := (z, ϕν(z))
sign(z)(ϕν(z)
− ϕν(k)) ≥ 0
for all k ∈ [min(0, z), max(0, z)]