Blow-up rates for a higher-order semilinear parabolic equation with nonlinear memory term

ABSTRACT

In this paper, we establish blow-up rates for a higher-order semilinear parabolic equation with nonlocal in time nonlinearity with no positive assumption on the solution. We also give Liouville-type theorem for higher-order semilinear parabolic equation with infinite memory nonlinear term which plays the main tools to prove our blow-up rate result. Finally, we study the well-posedness of mild solutions.

Keywords:

• Blow-up rate
• higher-order
• parabolic equation
• Riemann-Liouville fractional integrals and derivatives

2010 Mathematics Subject Classifications:

• Primary 35K25
• 35K30
• 35K55
• Secondary35B44
• 26A33
• 35A01

Acknowledgments

The author is supported by the Lebanese University research program.

Disclosure statement

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