Publication Cover
Applicable Analysis
An International Journal
Volume 92, 2013 - Issue 4
201
Views
13
CrossRef citations to date
0
Altmetric
Articles

Asymptotic analysis for blow-up solutions in parabolic equations involving variable exponents

&
Pages 651-664 | Received 26 Nov 2010, Accepted 13 Oct 2011, Published online: 14 Nov 2011

References

  • Friedman , A . 1969 . Partial Differential Equation of Parabolic Type , Englewood Cliffs, NJ : Prentice-Hall .
  • Acerbi , E and Mingione , G . 2002 . Regularity results for stationary electro-rheological fluids . Arch. Ration. Mech. Anal. , 164 : 213 – 259 .
  • Antontsev , SN and Rodrigues , JF . 2006 . On stationary thermo-rheological viscous flows . Ann. Univ. Ferrara, Sez. VII Sci. Mat. , 52 : 19 – 36 .
  • Rajagopal , K and Ružička , M . 2001 . Mathematical modelling of electro-rheological fluids . Contin. Mech. Thermodyn. , 13 : 59 – 78 .
  • Aboulaicha , R , Meskinea , D and Souissia , A . 2008 . New diffusion models in image processing . Comput. Math. Appl. , 56 : 874 – 882 .
  • Chen , Y , Levine , S and Rao , M . 2006 . Variable exponent, linear growth functionals in image restoration . SIAM J. Appl. Math. , 66 : 1383 – 1406 .
  • Levine , S , Chen , Y and Stanich , J . 2004 . Image restoration via nonstandard diffusion , Department of Mathematics and Computer Science, Duquesne University . Tech. Rep. ♯ 04–01
  • Pao , CV . 1992 . Nonlinear Parabolic and Elliptic Equations , New York : Plenum Press .
  • Samarskii , AA , Galaktionov , VA , Kurdyumov , SP and Mikhailov , AP . 1995 . Blow-up in Quasilinear Parabolic Equations , Berlin , , New York : Walter de Gruyter .
  • Pinasco , JP . 2009 . Blow-up for parabolic and hyperbolic problems with variable exponents . Nonlinear Anal. , 71 : 1094 – 1099 .
  • Antontsev , SN and Shmarev , S . 2010 . Blow-up of solutions to parabolic equations with nonstandard growth conditions . J. Comput. Appl. Math. , 234 : 2633 – 2645 .
  • Ferreira , R , de Pablo , A , Pérez-Llanos , M and Rossi , JD . Critical exponents for a semilinear parabolic equation with variable reaction , to appear in the Royal Society of Edinburgh Proceedings A (Mathematics). Available at http://mate.dm.uba.ar/~jrossi/FPPR-px-zamp.pdf
  • Bai , XL and Zheng , SN . 2011 . A semilinear parabolic system with coupling variable exponents . Ann. Mat. Pura Appl. , 190 : 525 – 537 .
  • Friedman , A and McLeod , B . 1985 . Blow-up of positive solutions of semilinear heat equations . Indiana Univ. Math. J. , 34 : 425 – 447 .
  • Friedman , A and Giga , Y . 1987 . A single point blow-up for solutions of semilinear parabolic systems . J. Fac. Sci. Univ. Tokyo Sect IA Math. , 34 : 65 – 79 .
  • Liu , WX . 1989 . The blow-up rate of solutions of semilinear heat equations . J. Diff. Eqns , 77 : 104 – 122 .
  • Souplet , Ph . 1999 . Uniform blow-up profile and boundary behaviour for diffusion equation with nonlocal nonlinear source . J. Differ. Eqns , 153 : 374 – 406 .

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.