Generalizing the Bardos-LeRoux-Nédélec boundary condition for ...
Generalizing the Bardos-LeRoux-Nédélec boundary condition for ...
Generalizing the Bardos-LeRoux-Nédélec boundary condition for ...
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The problem BLN <strong>condition</strong> & Alternatives Effective BC graph Definition Uniqueness Definition Bis Existence & Convergence of Approximations<br />
...<strong>the</strong> BLN <strong>condition</strong> and its justification...<br />
Example. Dimension one, Ω = [0, 1], <strong>the</strong> linear case :<br />
we consider ϕ(z) := z and <strong>the</strong> homogeneous Dirichlet datum u D := 0.<br />
In this case, we have <strong>the</strong> problem ut + ux = 0, u|t=0 = u0 and<br />
<strong>condition</strong> (BLN) reads :<br />
at <strong>the</strong> point x = 0, γu = 0;<br />
at <strong>the</strong> point x = 1, γu is arbitrary.<br />
Solutions are limits of vanishing viscosity approximation:<br />
u = limε↓0 u ε , u ε t + u ε x = εu ε xx, u ε |t=0 = u0 and u ε |x=0 = 0 = u ε |x=1.