Publication Cover
Applicable Analysis
An International Journal
Volume 92, 2013 - Issue 3
156
Views
12
CrossRef citations to date
0
Altmetric
Articles

Extinction and non-extinction for a polytropic filtration equation with a nonlocal source

&
Pages 636-650 | Received 12 Nov 2010, Accepted 13 Oct 2011, Published online: 14 Nov 2011

References

  • Kalashnikov , AS . 1974 . The nature of the propagation of perturbations in problems of non-linear heat conduction with absorption . USSR Comput. Math. Math. Phys. , 14 : 70 – 85 .
  • Gu , YG . 1994 . Necessary and sufficient conditions of extinction of solution on parabolic equations . Acta. Math. Sin. , 37 : 73 – 79 . in Chinese
  • Friedman , A and Herrero , Miguel A . 1987 . Extinction properties of semilinear heat equations with strong absorption . J. Math. Anal. Appl. , 124 : 530 – 546 .
  • Herrero , MA and Velazquez , JJL . 1992 . Approaching an extinction point in one-dimensional semilinear heat equations with strong absorptions . J. Math. Anal. Appl. , 170 : 353 – 381 .
  • Dibenedetto , E . 1993 . Degenerate Parabolic Equations , New York : Springer .
  • Yuan , HJ , Lian , SZ , Gao , WJ , Xu , XJ and Cao , CL . 2005 . Extinction and positive for the evolution p-Laplacian equation in R N . Nonlinear Anal. TMA , 60 : 1085 – 1091 .
  • Jin , CH , Yin , JX and Ke , YY . 2009 . Critical extinction and blow-up exponents for fast diffusive polytropic filtration equation with sources . Proc. Edinb. Math. Soc. , 52 : 419 – 444 .
  • Zhou , J and Mu , CL . 2009 . Critical blow-up and extinction exponents for non-Newton polytropic filtration equation with source . Bull. Korean Math. Soc. , 46 : 1159 – 1173 .
  • Berryman , JG and Holland , CJ . 1980 . Stability of the separable solution for fast diffusion . Arch. Ration. Mech. Anal. , 74 : 379 – 388 .
  • Ferreira , R and Vazquez , JL . 2001 . Extinction behavior for fast diffusion equations with absorption . Nonlinear Anal. , 43 : 943 – 985 .
  • Friedman , A and Kamin , S . 1980 . The asymptotic behavior of gas in an n-dimensional porous medium . Trans. Am. Math. Soc. , 262 : 551 – 563 .
  • Galaktionov , VA and King , JR . 2002 . Fast diffusion equation with critical Sobolev exponent in a ball . Nonlinearity , 15 : 173 – 188 .
  • Galaktionov , VA , Peletier , LA and Vazquez , JL . 2000 . Asymptotics of fast-diffusion equation with critical exponent . SIAM J. Math. Anal. , 31 : 1157 – 1174 .
  • Galaktionov , VA and Vazquez , JL . 1991 . symptotic behavior of nonlinear parabolic equations with critical exponents. A dynamical system approach . J. Funct. Anal. , 100 : 435 – 462 .
  • Galaktionov , VA and Vazquez , JL . 1994 . Extinction for a quasilinear heat equation with absorption: I. Technique of intersection comparison . Commun. Partial Differ. Eqns , 19 : 1075 – 1106 .
  • Galaktionov , VA and Vazquez , JL . 1994 . Extinction for a quasilinear heat equation with absorption II. A dynamical system approach . Commun. Partial Differ. Eqns , 19 : 1107 – 1137 .
  • Li , YX and Wu , JC . 2005 . Extinction for fast diffusion equations with nonlinear sources . Electron J. Differ. Eqns , 2005 : 1 – 7 .
  • Tian , Y and Mu , CL . 2008 . Extinction and non-extinction for a p-Laplacian equation with nonlinear source . Nonlinear Anal. , 69 : 2422 – 2431 .
  • Yin , JX , Li , J and Jin , CH . 2009 . Non-extinction and critical exponent for a polytropic filtration equation . Nonlinear. Anal. , 71 : 347 – 357 .
  • Yin , JX and Jin , CH . 2007 . Critical extinction and blow-up exponents for fast diffusive p-Laplacian with sources . Math. Method. Appl. Sci. , 30 ( 10 ) : 1147 – 1167 .
  • Wu , ZQ , Yin , JX and Wang , CP . 2006 . Elliptic and Parabolic Equations , New York, Singapore : World Scientific .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.