Publication Cover
Applicable Analysis
An International Journal
Volume 100, 2021 - Issue 6
172
Views
1
CrossRef citations to date
0
Altmetric
Articles

A Cauchy problem of parabolic equations with time-dependent coefficients

ORCID Icon, &
Pages 1272-1285 | Received 10 Apr 2019, Accepted 29 Jun 2019, Published online: 07 Jul 2019

References

  • Friedman A. Partial differential equations of parabolic type. Englewood Cliffs (NJ): Prentice Hall; 1964.
  • Uda Y. The critical exponent for a weakly coupled system of the generalized Fujita type reaction-diffusion equations. Z Angew Math Phys. 1995;46:366–383. doi: 10.1007/BF01003556
  • Cao XR, Bai XL, Zheng SN. Critical Fujita curve for a semilinear parabolic system with time-weighted sources. Appl Anal. 2014;933:597–605. doi: 10.1080/00036811.2013.794937
  • Bai XL, Zheng SN, Wang W. Critical exponent for parabolic system with time-weighted sources in bounded domain. J Funct Anal. 2013;265:941–952. doi: 10.1016/j.jfa.2013.05.023
  • Liu BC, Lin HY. A Cauchy problem of spatial-weighted reaction C diffusion equations. Appl Math Lett. 2019;92:128–133. doi: 10.1016/j.aml.2019.01.021
  • Brändle C, Quirós F, Rossi JD. The role of non-linear diffusion in non-simultaneous blow-up. J Math Anal Appl. 2005;308:92–104. doi: 10.1016/j.jmaa.2004.11.004
  • Du YN, Liu BC. Time-weighted blow-up profiles in a nonlinear parabolic system with Fujita exponent. Comput Math Appl. 2018;9283:0898–1221.
  • Hu B. Blow up theories for semilinear parabolic equations. Berlin: Springer-Verlarg; 2011. (Lecture notes in mathematics 1022).
  • Li LL, Sun HR, Zhang QG. Existence and nonexistence of global solutions for a semilinear reaction-diffusion system. J Math Anal Appl. 2017;445:97–124. doi: 10.1016/j.jmaa.2016.07.067
  • Pinsky RG. Existence and nonexistence of global solutions for ut=Δu+a(x)up in Rd. J Differ Equ. 1997;133:152–177. doi: 10.1006/jdeq.1996.3196
  • Chlebik M, Fila M. From critical exponents to blow-up rates for parabolic systems. Rendiconti Matematica. 1999;19:449–470.
  • Liu BC, Li FJ. Blow-up properties for heat equations coupled via different nonlinearities. J Math Anal Appl. 2008;347:294–303. doi: 10.1016/j.jmaa.2008.06.004

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.