An Application Of The Theory Of Scale Of Banach Spaces

Łukasz Dawidowski

Annales Mathematicae Silesianae (2015)

  • Volume: 29, Issue: 1, page 51-59
  • ISSN: 0860-2107

Abstract

top
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.

How to cite

top

Łukasz Dawidowski. "An Application Of The Theory Of Scale Of Banach Spaces." Annales Mathematicae Silesianae 29.1 (2015): 51-59. <http://eudml.org/doc/276906>.

@article{ŁukaszDawidowski2015,
abstract = {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.},
author = {Łukasz Dawidowski},
journal = {Annales Mathematicae Silesianae},
keywords = {scale of Banach spaces; parabolic equations},
language = {eng},
number = {1},
pages = {51-59},
title = {An Application Of The Theory Of Scale Of Banach Spaces},
url = {http://eudml.org/doc/276906},
volume = {29},
year = {2015},
}

TY - JOUR
AU - Łukasz Dawidowski
TI - An Application Of The Theory Of Scale Of Banach Spaces
JO - Annales Mathematicae Silesianae
PY - 2015
VL - 29
IS - 1
SP - 51
EP - 59
AB - 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.
LA - eng
KW - scale of Banach spaces; parabolic equations
UR - http://eudml.org/doc/276906
ER -

References

top
  1. [1] Adams R.A., Sobolev spaces, Academic Press, New York–San Francisco–London, 1975. Zbl0314.46030
  2. [2] Cholewa J.W., Dłotko T., Global attractors in abstract parabolic problems, Cambridge University Press, Cambridge, 2000. Zbl0954.35002
  3. [3] Dawidowski Ł., Scales of Banach spaces, theory of interpolation and their applications, Wydawnictwo Uniwersytetu Śląskiego, Katowice, 2012. Zbl1282.46001
  4. [4] Evans L.C., Partial differential equations, Graduate Studies in Mathematics 19, American Mathematical Society, Providence, Rhode Island, 1998. Zbl0902.35002
  5. [5] Gilbarg D., Trudinger N., Elliptic partial differential equations of second order, Reprint of the 1998 edition, Springer-Verlag, Berlin, 2001. Zbl1042.35002
  6. [6] Henry D., Geometric theory of semilinear parabolic equations, Lecture Notes in Mathematics 840, Springer-Verlag, Berlin, 1981. Zbl0456.35001
  7. [7] Komatsu H., Fractional powers of operators, Pacific J. Math. 19 (1966), 285–346. Zbl0154.16104
  8. [8] Yagi A., Abstract parabolic evolution equations and their applications, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2010. Zbl1190.35004

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.