An Application Of The Theory Of Scale Of Banach Spaces
Łukasz Dawidowski
Annales Mathematicae Silesianae, Tome 29 (2015), p. 51-59 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

The abstract Cauchy problem on scales of Banach space was considered by many authors. The goal of this paper is to show that the choice of the space on scale is significant. We prove a theorem that the selection of the spaces in which the Cauchy problem ut − Δu = u|u|s with initial–boundary conditions is considered has an influence on the selection of index s. For the Cauchy problem connected with the heat equation we will study how the change of the base space influents the regularity of the solutions.

Publié le : 2015-01-01
EUDML-ID : urn:eudml:doc:276906 
@article{bwmeta1.element.doi-10_1515_amsil-2015-0005,
     author = {\L ukasz Dawidowski},
     title = {An Application Of The Theory Of Scale Of Banach Spaces},
     journal = {Annales Mathematicae Silesianae},
     volume = {29},
     year = {2015},
     pages = {51-59},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_amsil-2015-0005}
}

Łukasz Dawidowski. An Application Of The Theory Of Scale Of Banach Spaces. Annales Mathematicae Silesianae, Tome 29 (2015) pp. 51-59. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_amsil-2015-0005/

[1] Adams R.A., Sobolev spaces, Academic Press, New York–San Francisco–London, 1975. | Zbl 0314.46030

[2] Cholewa J.W., Dłotko T., Global attractors in abstract parabolic problems, Cambridge University Press, Cambridge, 2000. | Zbl 0954.35002

[3] Dawidowski Ł., Scales of Banach spaces, theory of interpolation and their applications, Wydawnictwo Uniwersytetu Śląskiego, Katowice, 2012. | Zbl 1282.46001

[4] Evans L.C., Partial differential equations, Graduate Studies in Mathematics 19, American Mathematical Society, Providence, Rhode Island, 1998. | Zbl 0902.35002

[5] Gilbarg D., Trudinger N., Elliptic partial differential equations of second order, Reprint of the 1998 edition, Springer-Verlag, Berlin, 2001. | Zbl 1042.35002

[6] Henry D., Geometric theory of semilinear parabolic equations, Lecture Notes in Mathematics 840, Springer-Verlag, Berlin, 1981. | Zbl 0456.35001

[7] Komatsu H., Fractional powers of operators, Pacific J. Math. 19 (1966), 285–346. | Zbl 0154.16104

[8] Yagi A., Abstract parabolic evolution equations and their applications, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2010. | Zbl 1190.35004