On blow-up and asymptotic behavior of solutions for some semilinear parabolic systems of second order

Théodore K. Boni

Bollettino dell'Unione Matematica Italiana (2000)

  • Volume: 3-B, Issue: 2, page 375-409
  • ISSN: 0392-4041

How to cite

top

Boni, Théodore K.. "On blow-up and asymptotic behavior of solutions for some semilinear parabolic systems of second order." Bollettino dell'Unione Matematica Italiana 3-B.2 (2000): 375-409. <http://eudml.org/doc/195336>.

@article{Boni2000,
author = {Boni, Théodore K.},
journal = {Bollettino dell'Unione Matematica Italiana},
keywords = {nonlinear boundary conditions; global existence; blow-up set},
language = {eng},
month = {6},
number = {2},
pages = {375-409},
publisher = {Unione Matematica Italiana},
title = {On blow-up and asymptotic behavior of solutions for some semilinear parabolic systems of second order},
url = {http://eudml.org/doc/195336},
volume = {3-B},
year = {2000},
}

TY - JOUR
AU - Boni, Théodore K.
TI - On blow-up and asymptotic behavior of solutions for some semilinear parabolic systems of second order
JO - Bollettino dell'Unione Matematica Italiana
DA - 2000/6//
PB - Unione Matematica Italiana
VL - 3-B
IS - 2
SP - 375
EP - 409
LA - eng
KW - nonlinear boundary conditions; global existence; blow-up set
UR - http://eudml.org/doc/195336
ER -

References

top
  1. AMANN, H., Dynamic theory of quasilinear parabolic systems III global existence, Math. Z., 202, 2 (1989), 219-254. Zbl0702.35125MR1013086
  2. BONI, T. K., Sur l'explosion et le comportement asymptotique de la solution d'une équation parabolique semi-linéaire du second ordre, C. R. Acad. Paris, t. 326, Série I (1998), 317-322. Zbl0913.35069MR1648453
  3. DENG, K., Global existence and blow up for a system of heat equations with a nonlinear boundary conditions, Math. Meth. in the Appl. Sci., 18 (1995), 307-315. Zbl0822.35074MR1320001
  4. ESCOBEDO, M.- HERRERO, M. A., A semilinear parabolic system in a bounded domain, Ann. Mat. pura applicata, (IV), Vol. CLXV (1993), 315-336. Zbl0806.35088MR1271424
  5. ESCOBEDO, M.- LEVINE, H. A., Critical blow up and global existence for a weakly coupled system of reaction-diffusion equations, Arch. Rational Mech. Anal., 129 (1995), 47-100. Zbl0822.35068MR1328471
  6. ESCHER, J., Global existence and nonexistance for parabolic systems with nonlinear boundary conditions, Math. Ann., 284 (1989), 285-305. Zbl0652.35065MR1000112
  7. GANG, L.- SLEEMAN, B. D., Non-existence of global solutions to systems of semi-linear parabolic equations, Jour. of Diff. Equat., 104 (1993), 147-168. Zbl0816.35060MR1224124
  8. HOLLAND, C. J., Limiting behavior of a class of nonlinear reaction diffusion equations, Quaterly of Applied Mathematics, 3, Vol. XL (1982), 293-296. Zbl0506.35059MR678200
  9. HENRY, D., Geometric theory of semilinear parabolic equations, Lecture Notes in Mathematics, vol. 840, Springer (1981). Zbl0456.35001MR610244
  10. LEVINE, H. A. and PAYNE, L. E., Nonexistence theorems for the heat equation with nonlinear boundary conditions and for the porous medium equation backward in time, Jour. of Diff. Equat., 16 (1974), 319-334. Zbl0285.35035MR470481
  11. PROTTER, M. H.- WEINBERGER, H. F., Maximum principles in differential equations, Prentice Hall, Englewood Cliffs, NJ (1967). Zbl0153.13602MR219861
  12. ROSSI, J.- WOLANSKI, N., Blow-up vs. global existence for a semilinear reactiondiffusion system in a bounded domain, Commun. in PDE., 20 (11 and 12), (1995), 1991-2004. Zbl0851.35064MR1361728
  13. WALTER, W., Differential- und integral-ungleichungen, Springer, Berlin (1964). MR172076

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.