A Cauchy problem of parabolic equations with time-dependent coefficients

ABSTRACT

In this paper, we study a Cauchy problem of parabolic equations with time-dependent coefficients. The critical Fujita exponents are determined by the exponents of components and dimension of domain and the coefficients. Moreover, we give the optimal classification of blow-up solutions which discriminates simultaneous and non-simultaneous blow-up of two components. At last, simultaneous blow-up rates are obtained.

KEYWORDS:

• Critical Fujita exponent
• blow-up rate
• non-simultaneous blow-up
• variable coefficient

MSC (2010):

• 35K15
• 35K55
• 35B40

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This paper is supported by Shandong Provincial Natural Science Foundation of China [grant number ZR2017LA003].