Blow-up of nonnegative solutions to quasilinear parabolic inequalities

Stanislav I. Pohozaev; Alberto Tesei

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (2000)

  • Volume: 11, Issue: 2, page 99-109
  • ISSN: 1120-6330

Abstract

top
We investigate critical exponents for blow-up of nonnegative solutions to a class of parabolic inequalities. The proofs make use of a priori estimates of solutions combined with a simple scaling argument.

How to cite

top

Pohozaev, Stanislav I., and Tesei, Alberto. "Blow-up of nonnegative solutions to quasilinear parabolic inequalities." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 11.2 (2000): 99-109. <http://eudml.org/doc/252310>.

@article{Pohozaev2000,
abstract = {We investigate critical exponents for blow-up of nonnegative solutions to a class of parabolic inequalities. The proofs make use of a priori estimates of solutions combined with a simple scaling argument.},
author = {Pohozaev, Stanislav I., Tesei, Alberto},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Critical exponent; Parabolic inequalities; Blow-up; Global existence; nonexistence of global solutions; nonlinear capacity},
language = {eng},
month = {6},
number = {2},
pages = {99-109},
publisher = {Accademia Nazionale dei Lincei},
title = {Blow-up of nonnegative solutions to quasilinear parabolic inequalities},
url = {http://eudml.org/doc/252310},
volume = {11},
year = {2000},
}

TY - JOUR
AU - Pohozaev, Stanislav I.
AU - Tesei, Alberto
TI - Blow-up of nonnegative solutions to quasilinear parabolic inequalities
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2000/6//
PB - Accademia Nazionale dei Lincei
VL - 11
IS - 2
SP - 99
EP - 109
AB - We investigate critical exponents for blow-up of nonnegative solutions to a class of parabolic inequalities. The proofs make use of a priori estimates of solutions combined with a simple scaling argument.
LA - eng
KW - Critical exponent; Parabolic inequalities; Blow-up; Global existence; nonexistence of global solutions; nonlinear capacity
UR - http://eudml.org/doc/252310
ER -

References

top
  1. Fujita, H., On the Blowingup of Solutions of the Cauchy Problem for u t = △ ⁢ u + u 1 + α . J. Fac. Sci. Univ. Tokyo, 16A, 1966, 105-113. Zbl0163.34002
  2. Levine, H. A., The Role of Critical Exponents in Blowup Theorems. SIAM Rev., 32, 1990, 262-288. Zbl0706.35008MR1056055DOI10.1137/1032046
  3. Mitidieri, E. - Pohozaev, S. I., The Absence of Global Positive Solutions to Quasilinear Elliptic Inequalities. Dokl. Russ. Acad. Sci., 359, 1998, 456-460. Zbl0976.35100MR1668404
  4. Pohozaev, S. I., The Essentially Nonlinear Capacities Induced by Differential Operators. Dokl. Russ. Acad. Sci., 357, 1997, 592-594. Zbl0963.35056MR1608995
  5. Samarskii, A. A. - Galaktionov, V. A. - Kurdyumov, S. P. - Mikhailov, A. P., Blow-up in Quasilinear Parabolic Equations. GEM, 19, de Gruyter, Berlin1995. Zbl1020.35001MR1330922DOI10.1515/9783110889864.535

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.