Lower Bounds for Blow-Up Time of Reaction-Diffusion Equations With Gradient Terms and Nonlocal Terms

SHEN Xuhui

doi:10.21656/1000-0887.420155

Volume 43 Issue 4

Apr. 2022

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SHEN Xuhui. Lower Bounds for Blow-Up Time of Reaction-Diffusion Equations With Gradient Terms and Nonlocal Terms[J]. Applied Mathematics and Mechanics, 2022, 43(4): 469-476. doi: 10.21656/1000-0887.420155

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Lower Bounds for Blow-Up Time of Reaction-Diffusion Equations With Gradient Terms and Nonlocal Terms

doi: 10.21656/1000-0887.420155

SHEN Xuhui

School of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan 030006, P.R.China

Received Date: 2021-06-07
Rev Recd Date: 2021-08-19

Available Online: 2022-03-14

Publish Date: 2022-04-01

Abstract

Abstract

The research on the blow-up time of solutions to the reaction-diffusion equations has much theoretical significance. Moreover, it is closely related to practical problems such as production safety control, population density control and environmental chemotaxis control. The lower bounds for the blow-up time of solutions to a class of reaction-diffusion equations with gradient terms and nonlocal terms, were considered. Firstly, the region was assumed to be a bounded convex one with smooth boundary in the high-dimensional space. Secondly, through the establishment of suitable auxiliary functions, and with the 1st-order differential inequality and the Sobolev inequality, the lower bounds for the blow-up time were derived for finite-time blow-up occurences. Finally, 2 application examples illustrate the abstract results obtained with this method.
- reaction-diffusion equation,
- gradient term,
- nonlocal term,
- blow-up time

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References(20)

References

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