Some (new) counterexamples of parabolic systems

Jana Stará; Oldřich John

Commentationes Mathematicae Universitatis Carolinae (1995)

  • Volume: 36, Issue: 3, page 503-510
  • ISSN: 0010-2628

Abstract

top
We give examples of parabolic systems (in space dimension n ≥ 3 ) having a solution with real analytic initial and boundary values which develops the discontinuity in the interior of the parabolic cylinder.

How to cite

top

Stará, Jana, and John, Oldřich. "Some (new) counterexamples of parabolic systems." Commentationes Mathematicae Universitatis Carolinae 36.3 (1995): 503-510. <http://eudml.org/doc/247771>.

@article{Stará1995,
abstract = {We give examples of parabolic systems (in space dimension $n\ge 3 $) having a solution with real analytic initial and boundary values which develops the discontinuity in the interior of the parabolic cylinder.},
author = {Stará, Jana, John, Oldřich},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {parabolic systems; regularity of weak solutions; blow up; regularity of weak solutions; blow up; parabolic systems},
language = {eng},
number = {3},
pages = {503-510},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Some (new) counterexamples of parabolic systems},
url = {http://eudml.org/doc/247771},
volume = {36},
year = {1995},
}

TY - JOUR
AU - Stará, Jana
AU - John, Oldřich
TI - Some (new) counterexamples of parabolic systems
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1995
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 36
IS - 3
SP - 503
EP - 510
AB - We give examples of parabolic systems (in space dimension $n\ge 3 $) having a solution with real analytic initial and boundary values which develops the discontinuity in the interior of the parabolic cylinder.
LA - eng
KW - parabolic systems; regularity of weak solutions; blow up; regularity of weak solutions; blow up; parabolic systems
UR - http://eudml.org/doc/247771
ER -

References

top
  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. (1986) MR0843425
  2. Struwe M., A counterexample in regularity theory for parabolic systems, Czech. Math. Journal 34 109 (1984), 183-188. (1984) Zbl0573.35053MR0743484
  3. Kalita E., On the Hölder continuity of solutions of nonlinear parabolic systems, Comment. Math. Univ. Carolinae 35 4 (1994), 675-680. (1994) Zbl0814.35011MR1321237
  4. Koshelev A.I., Regularity of solutions of quasilinear elliptic systems, Uspekhi Mat. Nauk 33 (1978), 3-49. (1978) MR0510669
  5. Koshelev A.I., Chelkak S.I., Regularity of solutions of quasilinear elliptic systems, Teubner-Texte zur Mathematik, Band 77 (1985). (1985) Zbl0581.35003MR0825485
  6. John O., Malý J., Stará J., Nowhere continuous solutions to elliptic systems, Comment. Math. Univ. Carolinae 30 1 (1989), 33-43. (1989) MR0995699
  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). MR1118218
  8. Gröger K., Rehberg J., Local existence and uniqueness of solutions to nonsmooth parabolic systems, to appear. 
  9. John O., Stará J., Remark on regularity of solutions to parabolic systems in two space dimensions, to appear. 
  10. De Giorgi E., Un esempio di estremali discontinue per un problema variazionale di tipo ellittico, Boll. UMI 4 (1968), 135-137. (1968) MR0227827
  11. Koshelev A.I., Regularity of solutions for some quasilinear parabolic systems, Math. Nachr. 162 (1993), 59-88. (1993) Zbl0811.35064MR1239576

NotesEmbed ?

top

You must be logged in to post comments.