Lower Bounds of the Blow-up Time for a Class of Reaction Diffusion Equations

XU Ran; TIAN Ya; QIN Yao

doi:10.21656/1000-0887.410160

Volume 42 Issue 1

Jan. 2021

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XU Ran, TIAN Ya, QIN Yao. Lower Bounds of the Blow-up Time for a Class of Reaction Diffusion Equations[J]. Applied Mathematics and Mechanics, 2021, 42(1): 113-122. doi: 10.21656/1000-0887.410160

Citation:

XU Ran, TIAN Ya, QIN Yao. Lower Bounds of the Blow-up Time for a Class of Reaction Diffusion Equations[J]. Applied Mathematics and Mechanics, 2021, 42(1): 113-122. doi: 10.21656/1000-0887.410160

Citation:

XU Ran, TIAN Ya, QIN Yao. Lower Bounds of the Blow-up Time for a Class of Reaction Diffusion Equations[J]. Applied Mathematics and Mechanics, 2021, 42(1): 113-122. doi: 10.21656/1000-0887.410160

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Lower Bounds of the Blow-up Time for a Class of Reaction Diffusion Equations

doi: 10.21656/1000-0887.410160

School of Science, Chongqing University of Posts and Telecommunications,Chongqing 400065, P.R.China

Received Date: 2020-06-03
Rev Recd Date: 2020-07-11
Publish Date: 2021-01-01

Abstract

Abstract

The blow-up behaviors in a bounded domain were considered for a class of reaction diffusion equations with nonlinear nonlocal heat sources and time-dependent-coefficient heat sink, under the Dirichlet, the Neumann and the Robin boundary conditions respectively.Through construction of auxiliary functions and appropriate conditions for the time-dependent coefficients, with the Sobolev inequality, the H?lder inequality and the Payne and Schaefer integral inequality etc., the lower bounds of the blow-up time of solutions were given for the blow-up occurring in a finite time.
- nonlocal problem,
- time-dependent coefficient,
- lower bound of the blow-up time

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References(14)

References

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