Blow-Up Behaviors of Solutions to Reaction-Diffusion Equations With Nonlocal Sources and Variable Exponents

TIAN Ya; QIN Yao; XIANG Jing

doi:10.21656/1000-0887.420180

Volume 43 Issue 10

Oct. 2022

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TIAN Ya, QIN Yao, XIANG Jing. Blow-Up Behaviors of Solutions to Reaction-Diffusion Equations With Nonlocal Sources and Variable Exponents[J]. Applied Mathematics and Mechanics, 2022, 43(10): 1177-1184. doi: 10.21656/1000-0887.420180

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Blow-Up Behaviors of Solutions to Reaction-Diffusion Equations With Nonlocal Sources and Variable Exponents

doi: 10.21656/1000-0887.420180

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

Received Date: 2021-07-01
Accepted Date: 2021-09-29
Rev Recd Date: 2021-09-09

Available Online: 2022-09-24

Publish Date: 2022-10-31

Abstract

Abstract

The blow-up problems of the solutions are considered for reaction-diffusion equations with nonlocal sources and variable exponents. Firstly, the local existence and uniqueness of solutions to the problem were proved under the fixed-point theorem. Secondly, by means of the super- and sub-solution method, some sufficient conditions for the occurrence of finite-time blow-up were determined under the homogeneous Dirichlet boundary conditions, i.e., the variable exponent is positive and the initial value is large enough. Moreover, the estimates of upper and lower bounds of the blow-up time were given.
- nonlocal source,
- variable exponent,
- blow-up in finite time,
- upper and lower bounds of the blow-up time

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References(16)

References

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