A new sufficient condition for blow-up of solutions to a class of parabolic equations

Abstract

In this paper, a new sufficient condition under which the solutions to a classical parabolic equation blow up is established. During this process, through constructing a new functional which falls between the energy and Nehari functionals, we also get a larger blow-up set.

Keywords:

• parabolic equation
• blow-up
• Nehari functional
• energy functional

AMS Subject Classifications:

• 35K05
• 35B44

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

Partially supported by National Natural Science Foundation of China [grant number 11071149], [grant number 11301313]; Science Council of Shanxi Province [2012011004-2], [2013021001-4], [2014021009-1], [2015021007].