Lifespan of solutions to a parabolic type Kirchhoff equation with time-dependent nonlinearity

Haixia Li

doi:10.3934/eect.2020088

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2021, Volume 10, Issue 4: 723-732. Doi: 10.3934/eect.2020088

This issue Previous Article Deterministic control of stochastic reaction-diffusion equations Next Article S-asymptotically

$ \omega $

-periodic mild solutions and stability analysis of Hilfer fractional evolution equations

Lifespan of solutions to a parabolic type Kirchhoff equation with time-dependent nonlinearity

Haixia Li^,

School of Mathematics, Changchun Normal University, Changchun, 130032, China

^* Corresponding author: Haixia Li
^* Corresponding author: Haixia Li

Received: March 31, 2020

Revised: June 30, 2020

Early access: August 2020

Published: December 2021

The author is supported by NSFC (11626044), by NSF of Changchun Normal University (2015-002) and by Scientific Research Foundation for Talented Scholars of Changchun Normal University (RC2016-008)

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Abstract

In this paper, an initial boundary value problem for a parabolic type Kirchhoff equation with time-dependent nonlinearity is considered. A new blow-up criterion for nonnegative initial energy is given and upper and lower bounds for the blow-up time are also derived. These results partially generalize some recent ones obtained by Han and Li in [Threshold results for the existence of global and blow-up solutions to Kirchhoff equations with arbitrary initial energy, Computers and Mathematics with Applications, 75(2018), 3283-3297].

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Mathematics Subject Classification: Primary: 35K20; Secondary: 35K59.

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References

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