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Applicable Analysis
An International Journal
Volume 99, 2020 - Issue 6
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Articles

Blow-up analysis for a nonlocal reaction-diffusion system with time-dependent coefficients

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Pages 976-999 | Received 18 Mar 2018, Accepted 10 Aug 2018, Published online: 05 Sep 2018

References

  • Smoller J. Shock waves and reaction-diffusion equations. 2nd ed. New York-Berlin: Springer-Verlag; 1994.
  • Hu B. Blow-up theories for semilinear parabolic equations, lecture notes in mathematics. Heidelberg: Springer; 2011.
  • Quittner R, Souplet P. Superlinear parabolic problems: blow-up, global existence and steady states. Basel: Birkhauser; 2007.
  • Blow-up in nonlocal reaction-diffusion equations. SIAM J Math Anal. 1998;29(6):1301–1334. doi: 10.1137/S0036141097318900
  • Escobedo M, Levine HA. Critical blowup and global existence numbers for weakly coupled system of reaction-diffusion equations. Arch Rational Mech Anal. 1995;129:47–100. doi: 10.1007/BF00375126
  • Levine HA. Nonexistence of global weak solutions to some properly and improperly posed problems of mathematical physics: the method of unbounded Fourier coefficients. Math Ann. 1975;214(3):205–220. doi: 10.1007/BF01352106
  • Song JC. Lower bounds for the blow-up time in a non-local reaction-diffusion problem. Appl Math Lett. 2011;24:793–796. doi: 10.1016/j.aml.2010.12.042
  • Liu Y. Lower bounds for the blow-up time in a non-local reaction diffusion problem under nonlinear boundary conditions. Math Comput Model. 2013;57:926–931. doi: 10.1016/j.mcm.2012.10.002
  • Tang GS, Li YF, Yang XT. Lower bounds for the blow-up time of the nonlinear non-local reaction diffusion problems in RN(N≥3). Bound Value Probl. 2014;2014:265–269. doi: 10.1186/s13661-014-0265-5
  • Song XF, Lv XS. Bounds for the blowup time and blowup rate estimates for a type of parabolic equations with weighted source. Appl Math Comput. 2014;236:78–92.
  • Ma LW, Fang ZB. Blow-up phenomena for a semilinear parabolic equation with weighted inner absorption under nonlinear boundary flux. Math Meth Appl Sci. 2017;40:115–128. doi: 10.1002/mma.3971
  • Ma LW, Fang ZB. Blow-up analysis for a reaction-diffusion equation with weighted nonlocal inner absorptions under nonlinear boundary flux. Nonlinear Anal RWA. 2016;32:338–354. doi: 10.1016/j.nonrwa.2016.05.005
  • Ma LW, Fang ZB. Blow-up analysis for a nonlocal reaction-diffusion equation with Robin boundary conditions. Taiwanese J Math. 2017;21(1):131–150. doi: 10.11650/tjm.21.2017.7380
  • Ma LW, Fang ZB. Lower bounds of the blow-up time for reaction-diffusion equation with weighted nonlocal source and Robin boundary conditions. Math Phys. 2017;37A(1):146–157.
  • Payne LE, Philippin GA. Blow-up phenomena in parabolic problems with time-dependent coefficients under Neumann boundary conditions. Proc Roy Soc Edinburgh Sec A. 2012;142(3):625–631. doi: 10.1017/S0308210511000485
  • Payne LE, Philippin GA. Blow-up phenomena in parabolic problems with time dependent coefficients under Dirichlet boundary conditions. Proc Am Math Soc. 2013;141(7):2309–2318. doi: 10.1090/S0002-9939-2013-11493-0
  • Fang ZB, Wang YX. Blow-up analysis for a semilinear parabolic equation with time-dependent coefficients under nonlinear boundary flux. Z Angew Math Phys. 2015;66:2525–2541. doi: 10.1007/s00033-015-0537-7
  • Liu ZQ, Fang ZB. Blow-up phenomena for a nonlocal quasilinear parabolic equation with time-dependent coefficients under nonlinear boundary flux. Discrete Contin Dyn Syst Ser B. 2016;21(10):3619–3635. doi: 10.3934/dcdsb.2016113
  • Wang YX, Fang ZB. Lower bounds for blow-up time in nonlocal parabolic problem under Robin boundary conditions. Appl Anal. 2018:12 p. doi: 10.1080/00036811.2018.1424329.
  • Payne LE, Song JC. Lower bounds for blow-up in a model of chemotaxis. J Math Anal Appl. 2012;385:672–676. doi: 10.1016/j.jmaa.2011.06.086
  • Xu XJ, Ye Z. Life span of solutions with large initial data for a class of coupled parabolic systems. Z Angew Math Phys. 2013;64:705–717. doi: 10.1007/s00033-012-0255-3
  • Payne LE, Philippin GA. Blow-up phenomena for a class of parabolic systems with time dependent coefficients. Appl Math. 2012;3:325–330. doi: 10.4236/am.2012.34049
  • Tao XY, Fang ZB. Blow-up phenomena for a nonlinear reaction-diffusion system with time dependent coefficients. Comput Math Appl. 2017;74:2520–2528. doi: 10.1016/j.camwa.2017.07.037
  • Bao AG, Song XF. Bounds for the blowup time of the solution to a parabolic system with nonlocal factors in nonlinearities. Comput Math Appl. 2016;71:723–729. doi: 10.1016/j.camwa.2015.12.029
  • Wang N, Song XF, Lv XS. Estimates for the blowup time of a combustion model with nonlocal heat sources. J Math Anal Appl. 2016;436:1180–1195. doi: 10.1016/j.jmaa.2015.12.025
  • Li FC, Huang SX, Xie CH. Global existence and blow-up of solutions to a nonlocal reaction-diffusion system. Discrete Contin Dyn Syst. 2003;9(6):1519–1532. doi: 10.3934/dcds.2003.9.1519
  • Souplet P. Single-point blow-up for a semilinear parabolic system. J Eur Math Soc. 2009;11:169–188. doi: 10.4171/JEMS/145
  • Burczak J, CiesLak T, Morales-Rodrigo C. Global existence vs. blow-up in a fully parabolic quasilinear 1D Keller-Segel system. Nonlinear Anal. 2012;75:5215–5228. doi: 10.1016/j.na.2012.04.038
  • Brezis H. Functional analysis, Sobolev spaces and partial differential equations. New York: Springer-Verlag; 2011.

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