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Applicable Analysis
An International Journal
Volume 96, 2017 - Issue 4
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Articles

Blow-up solutions for nonlinear reaction diffusion equations under Neumann boundary conditions

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Pages 549-562 | Received 07 Aug 2015, Accepted 15 Jan 2016, Published online: 22 Feb 2016

References

  • Straughan B. Explosive instabilities in mechanics. Berlin: Spring-Verlag; 1988.
  • Samarskii AA, Galaktionov VA, Kurdyumov SP, et al. Blow-up in problems for quasilinear parabolic equations. Moscow: Nauka; 1987. Russian. English translation, Berlin: Walter de Gruyter; 1995.
  • Quittner P, Souplet P. Superlinear parabolic problems: Blow-up, global existence and steady states, Birkhäuser advanced texts. Basel: Birkhäuser; 2007.
  • Levine HA. The role of critical exponents in blow-up theorems. SIAM Rev. 1990;32:262–288.
  • Bandle C, Brunner H. Blow-up in diffusion equations. A survey. J. Comput. Appl. Math. 1998;97:3–22.
  • Deng K, Levine HA. The role of critical exponents in blow-up theorems: the sequel. J. Math. Anal. Appl. 2000;243:85–126.
  • Galaktionov VA, Vázquez JL. The problem of blow-up in nonlinear parabolic equations. Discrete Contin. Dyn. Syst. 2002;8:399–433.
  • Zhang HL. Blow-up solutions and global solutions for nonlinear parabolic problems. Nonlinear Anal. TMA. 2008;69:4567–4574.
  • Zhang LL, Zhang N, Li LX. Blow-up solutions and global existence for a kind of quasilinear reaction-diffusion equations. Z. Anal. Anwend. 2014;33:247–258.
  • Payne LE, Schaefer PW. Lower bounds for blow-up time in parabolic problems under Neumann conditons. Appl. Anal. 2006;85:1301–1311.
  • Payne LE, Schaefer PW. Bounds for blow-up time for the heat equation under nonlinear boundary conditions. Proc. Roy. Soc. Edinburgh Sect. A. 2009;139:1289–1296.
  • Payne LE, Philippin GA, Vernier-Piro S. Blow-up phenomena for a semilinear heat equation with nonlinear boundary condition. II. Nonlinear Anal. 2010;73:971–978.
  • Payne LE, Philippin GA. Blow-up phenomena in parabolic problems with time dependent coefficients under Dirichlet boundary conditions. Proc. Am. Math. Soc. 2013;142:2309–2318.
  • Enache C. Blow-up, global existence and exponential decay estimates for a class of quasilinear parabolic problems. Nonlinear Anal. TMA. 2008;69:2864–2874.
  • Enache C. Blow-up phenomena for a class of quasilinear parabolic problems under Robin boundary condition. Appl. Math. Lett. 2011;24:288–292.
  • Ding JT. Global and blow-up solutions for nonlinear parabolic equations with Robin boundary conditions. Comput. Math. Appl. 2013;65:1808–1822.
  • Protter MH, Weinberger HF. Maximum principles in differential equations. Englewood Cliffs: Prentice-Hall; 1967.
  • Payne LE. Blow-up phenomena in parabolic problems with time-dependent coefficients under Neumann boundary conditions. Proc. Roy. Soc. Edinburgh Sect. A. 2012;142:625–631.
  • Enache C. Lower bounds for blow-up time in some non-linear parabolic problems under Neumann boundary conditions. Glasg. Math. J. 2011;53:569–575.
  • Gao XY, Ding JT, Guo BZ. Blow-up and global solutions for quasilinear parabolic equations with Neumann boundary conditions. Appl. Anal. 2009;88:183–191.
  • Ding JT, Guo BZ. Blow-up and global existence for nonlinear parabolic equations with Neumann boundary conditions. Comput. Math. Appl. 2010;60:670–679.
  • Qu CY, Bai XL, Zheng SN. Blow-up versus extinction in a nonlocal p-Laplace equation with Neumann boundary conditions. J. Math. Anal. Appl. 2014;412:326–333.

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