Non-simultaneous blow-up profile and boundary layer estimate in nonlinear parabolic problems

ABSTRACT

This paper deals with homogeneous Dirichlet problems of localized parabolic equations with different diffusion, where reaction terms are the product of the three components of solutions. According to the nontrivial coupled relationship, different non-simultaneous and simultaneous blow-up criteria are proposed for the three components. Then we show non-simultaneous blow-up profile and boundary layer estimates of solutions with or without standard growth conditions on the localized sources near blow-up time.

COMMUNICATED BY:

• D. Cao

KEYWORDS:

• Non-simultaneous blow-up
• blow-up profile
• boundary layer
• parabolic equations

MSC (2010):

• 35K05
• 35K60
• 35B40
• 35B33
• 65N25

Acknowledgments

The authors would like to thank the anonymous Referees and the Editors for valuable suggestions improving the first version of this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This paper is partially supported by NNSF of China, Shandong Provincial Natural Science Foundation, China [grant numbers ZR2016AM12, ZR2017LA003], and the Fundamental Research Funds for the Central Universities.