| Title:
|
Some (new) counterexamples of parabolic systems (English) |
| Author:
|
Stará, Jana |
| Author:
|
John, Oldřich |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
36 |
| Issue:
|
3 |
| Year:
|
1995 |
| Pages:
|
503-510 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We give examples of parabolic systems (in space dimension $n\geq 3 $) having a solution with real analytic initial and boundary values which develops the discontinuity in the interior of the parabolic cylinder. (English) |
| Keyword:
|
parabolic systems |
| Keyword:
|
regularity of weak solutions |
| Keyword:
|
blow up |
| MSC:
|
35B65 |
| MSC:
|
35D10 |
| MSC:
|
35K40 |
| MSC:
|
35K50 |
| MSC:
|
35K55 |
| idZBL:
|
Zbl 0846.35024 |
| idMR:
|
MR1364491 |
| . |
| Date available:
|
2009-01-08T18:19:43Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118779 |
| . |
| Reference:
|
[1] Stará J., John O., Malý J.: Counterexample to the regularity of weak solution of the quasilinear parabolic systems.Comment. Math. Univ. Carolinae 27 1 (1986), 123-136. MR 0843425 |
| Reference:
|
[2] Struwe M.: A counterexample in regularity theory for parabolic systems.Czech. Math. Journal 34 109 (1984), 183-188. Zbl 0573.35053, MR 0743484 |
| Reference:
|
[3] Kalita E.: On the Hölder continuity of solutions of nonlinear parabolic systems.Comment. Math. Univ. Carolinae 35 4 (1994), 675-680. Zbl 0814.35011, MR 1321237 |
| Reference:
|
[4] Koshelev A.I.: Regularity of solutions of quasilinear elliptic systems.Uspekhi Mat. Nauk 33 (1978), 3-49. MR 0510669 |
| Reference:
|
[5] Koshelev A.I., Chelkak S.I.: Regularity of solutions of quasilinear elliptic systems.Teubner-Texte zur Mathematik, Band 77 (1985). Zbl 0581.35003, MR 0825485 |
| Reference:
|
[6] John O., Malý J., Stará J.: Nowhere continuous solutions to elliptic systems.Comment. Math. Univ. Carolinae 30 1 (1989), 33-43. MR 0995699 |
| Reference:
|
[7] Nečas J., Šverák V.: On regularity of solutions of nonlinear parabolic systems.Annali Scuola Norm. Sup. Pisa, Ser. IV, Vol. XVIII, Fasc. 1 (1991). MR 1118218 |
| Reference:
|
[8] Gröger K., Rehberg J.: Local existence and uniqueness of solutions to nonsmooth parabolic systems.to appear. |
| Reference:
|
[9] John O., Stará J.: Remark on regularity of solutions to parabolic systems in two space dimensions.to appear. |
| Reference:
|
[10] De Giorgi E.: Un esempio di estremali discontinue per un problema variazionale di tipo ellittico.Boll. UMI 4 (1968), 135-137. MR 0227827 |
| Reference:
|
[11] Koshelev A.I.: Regularity of solutions for some quasilinear parabolic systems.Math. Nachr. 162 (1993), 59-88. Zbl 0811.35064, MR 1239576 |
| . |
