Critical Fujita curve for a semilinear parabolic system with time-weighted sources

Abstract

This paper studies the Fujita phenomena for the Cauchy problem to semilinear parabolic equations coupled via the time-weighted sources . The critical curve is determined for a wider range of parameters, where with . In particular, the decay cases of and are also included.

Keywords:

• Fujita phenomenon
• critical curve
• global solution
• non-global solution
• time-weighted sources
• semilinear parabolic system

AMS Subject Classifications:

• 35B33
• 35K55

Acknowledgments

Supported by the National Natural Science Foundation of China (11171048). The second author is also partially supported by the Shanghai Postdoctoral Sustentation Fund of China (13R21412600) with the current address: Center for PDE, East China Normal University, Shanghai, China.