Fujita phenomenon in higher-order parabolic equation with nonlocal term

Abstract

This paper considers the Cauchy problem for a higher-order semilinear parabolic equation with nonlocal term in , where , , , and . We obtain the critical Fujita exponent to the problem, in the sense that every nontrivial solution blows up in finite time whenever , and there are both global and non-global solutions if .

Keywords:

• Higher-order diffusion
• nonlocal source
• global solutions
• blow-up

AMS Subject Classifications:

• 35B33
• 35K30

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 11501438], [grant number 11601412], [grant number 11526161]; the Natural Science Basic Research Plan in Shaanxi Province of China [grant number 2015JQ1014].