Flux Condition Induced by Concentrated Reactions

Flux terms and Robin boundary conditions as limit of reactions and potentials concentrating at the boundary

“…Observe that earlier versions of this work, containing weaker results can be found in [5,6]. Also, [7], contains some related results for some nonlinear eigenvalue problems.…”

Boundary feedback as a singular limit of damped hyperbolic problems with terms concentrating at the boundary

“…, we can apply the Corollary 3.2 pag 194 from [6] with r = z = 2 to obtain that u ε 0 → u 0 0 in the Bessel space H s,2 (Ω) for any s < 3 2 and u 0 0 is the unique solution of limit elliptic problem −∆z (20) holds, see Remark 2. Since we also have f ∈ W 1,1 ((0, T ), L 2 (Ω)) and g ∈ H 1 ((0, T ), L 2 (Γ)), we get the result about u 0 (t).…”

“…The following lemma is a particular case of a result proved in [6] and basically states that concentrated functions behave as traces.…”

“…Different problems with concentrating terms near the boundary have been considered before. For example linear elliptic problems have been studied in [6]. Nonlinear elliptic problems, some including oscillations in the boundary, have been considered in [7], [5], [2]; see also [19].…”