Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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NEW BLOW-UP CRITERIA FOR A NONLOCAL REACTION-DIFFUSION SYSTEM

  • Kim, Eun-Seok (Department of Mathematics, Chonnam National University, Institute for General Education, Sunchon National University)
  • Received : 2021.06.11
  • Accepted : 2021.07.09
  • Published : 2021.12.25
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Abstract

Blow-up phenomena for a nonlocal reaction-diffusion system with time-dependent coefficients are investigated under null Dirichlet boundary conditions. Using Kaplan's method with the comparison principle, we establish new blow-up criteria and obtain the upper bounds for the blow-up time of the solution under suitable measure sense in the whole-dimensional space.

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References

  1. A.G. Bao, X.F. Song, Bounds for the blowup time of the solution to a parabolic system with nonlocal factors in nonlinearities, Comput. Math. Appl. 71 (2016) 723-729. https://doi.org/10.1016/j.camwa.2015.12.029
  2. M. Escobedo, M.A. Herrero, A semilinear parabolic system in a bounded domain, Ann. Mat. Pura Appl. 165(4) (1993) 315-336. https://doi.org/10.1007/BF01765854
  3. B. Hu, Blow-Up Theories for Semilinear Parabolic Equations, Lecture Notes in Mathematics, Springer, Heidelberg, 2011.
  4. L.E. Payne, G.A. Philippin, Blow-up phenomena for a class of parabolic systems with time dependent coefficients, Appl. Math. 3 (2012) 325-330. https://doi.org/10.4236/am.2012.34049
  5. R. Quittner, P. Souplet, Superlinear parabolic problems: Blow-up, global existence and steady states, Birkhauser, Basel, 2007.
  6. J. Smoller, Shock Waves and Reaction-Diffusion Equations, second edition, Springer-Verlag, 1994.
  7. Ph. Souplet, Blow-up in nonlocal reaction-diffusion equations, SIAM J. Math. Anal. 29(6) (1998) 1301-1334. https://doi.org/10.1137/S0036141097318900
  8. X.Y. Tao, Z.B. Fang, Blow-up phenomena for a nonlinear reaction-diffusion system with time dependent coefficients, Comput. Math. Appl. 74 (2017) 2520-2528. https://doi.org/10.1016/j.camwa.2017.07.037
  9. X.J. Xu, Z. Ye, Life span of solutions with large initial data for a class of coupled parabolic systems, Z. Angew. Math. Phys. 64 (2013) 705-717. https://doi.org/10.1007/s00033-012-0255-3