On one-parameter continuous family of pairs of complementary boundary conditions'
Artykuł w czasopiśmie
MNiSW
100
Lista 2021
| Status: | |
| Autorzy: | Bobrowski Adam, Ratajczyk Elżbieta |
| Dyscypliny: | |
| Aby zobaczyć szczegóły należy się zalogować. | |
| Rok wydania: | 2022 |
| Wersja dokumentu: | Drukowana | Elektroniczna |
| Język: | angielski |
| Wolumen/Tom: | 266 |
| Strony: | 81 - 92 |
| Impact Factor: | 0,8 |
| Web of Science® Times Cited: | 1 |
| Scopus® Cytowania: | 1 |
| Bazy: | Web of Science | Scopus |
| Efekt badań statutowych | NIE |
| Materiał konferencyjny: | NIE |
| Publikacja OA: | NIE |
| Abstrakty: | angielski |
| Let C[0,∞] be the space of continuous functions on the right half-axis R+ with finite limits at ∞, and let C[−∞,∞] be the space of continuous functions on the entire R that have finite limits at both −∞ and ∞. It has been known for some time that classical Feller–Wentzell boundary conditions for the Laplace operator in C[0,∞] are in one-to-one correspondence with certain subspaces of continuous functions on R that are invariant under the basic cosine family and the heat semigroup. In particular, the Robin boundary condition f′(0)=γf(0), where γ≥0 is a parameter, is linked with the subspace CγR⊂C[−∞,∞] of those f that satisfy f(−x)=f(x)−2γ∫x0e−γ(x−y)f(y)dy for x≥0. In this paper we find a natural operator Pγ that projects C[−∞,∞] onto CγR and with its help prove a surprising result saying that, for γ>0, CγR is complemented by the subspace CγF⊂C[−∞,∞] linked with the particular case of Feller–Wentzell boundary conditions describing slowly reflecting boundary (or sticky boundary), that is, with the condition f”(0)=γf′(0). |
