A semigroup related to a convex combination of boundary conditions obtained as a result of averaging other semigroups
Artykuł w czasopiśmie
MNiSW
30
Lista A
| Status: | |
| Autorzy: | Banasiak Jacek, Bobrowski Adam |
| Rok wydania: | 2015 |
| Wersja dokumentu: | Drukowana | Elektroniczna |
| Język: | angielski |
| Numer czasopisma: | 1 |
| Wolumen/Tom: | 15 |
| Strony: | 223 - 237 |
| Data nominalna: | 2014 |
| Web of Science® Times Cited: | 5 |
| Scopus® Cytowania: | 8 |
| Bazy: | Web of Science | Scopus | MathSciNet | Web of Science | SCOPUS | Zentralblatt Math |
| Efekt badań statutowych | NIE |
| Materiał konferencyjny: | NIE |
| Publikacja OA: | TAK |
| Licencja: | |
| Sposób udostępnienia: | Witryna wydawcy |
| Wersja tekstu: | Ostateczna wersja opublikowana |
| Czas opublikowania: | W momencie opublikowania |
| Abstrakty: | angielski |
| Let α be a bounded linear operator in a Banach space X , and let A be a closed operator in this space. Suppose that for Φ1,Φ2 mapping D(A) to another Banach space Y , A|kerΦ1 and A|kerΦ2 are generators of strongly continuous semigroups in X . Assume finally that A|kerΦa , where Φa=Φ1α+Φ2β and β=IX−α , is a generator also. In the case where X is an L 1-type space, and α is an operator of multiplication by a function 0≤α≤1 , it is tempting to think of the later semigroup as describing dynamics which, while at state x, is subject to the rules of A|kerΦ1 with probability α(x) and is subject to the rules of A|kerΦ2 with probability β(x)=1−α(x) . We provide an approximation (a singular perturbation) of the semigroup generated by A|kerΦa by semigroups built from those generated by A|kerΦ1 and A|kerΦ2 that supports this intuition. This result is motivated by a model of dynamics of Solea solea (Arino et al. in SIAM J Appl Math 60(2):408–436, 1999–2000; Banasiak and Goswami in Discrete Continuous Dyn Syst Ser A 35(2):617–635, 2015; Banasiak et al. in J Evol Equ 11:121–154, 2011, Mediterr J Math 11(2):533–559, 2014; Banasiak and Lachowicz in Methods of small parameter in mathematical biology, Birkhäuser, 2014; Sanchez et al. in J Math Anal Appl 323:680–699, 2006) and is, in a sense, dual to those of Bobrowski (J Evol Equ 7(3):555–565, 2007), Bobrowski and Bogucki (Stud Math 189:287–300, 2008), where semigroups generated by convex combinations of Feller’s generators were studied. |
