Quenching phenomenon of a time‐fractional diffusion equation with singular source term |
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| Authors: | Yufeng Xu Zhoushun Zheng |
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| Affiliation: | Department of Applied Mathematics, Central South University, Changsha, China |
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| Abstract: | In this paper, a time‐fractional diffusion equation with singular source term is considered. The Caputo fractional derivative with order 0<α ?1 is applied to the temporal variable. Under specific initial and boundary conditions, we find that the time‐fractional diffusion equation presents quenching solution that is not globally well‐defined as time goes to infinity. The quenching time is estimated by using the eigenfunction of linear fractional diffusion equation. Moreover, by implementing a finite difference scheme, we give some numerical simulations to demonstrate the theoretical analysis. Copyright © 2017 John Wiley & Sons, Ltd. |
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| Keywords: | quenching phenomenon fractional diffusion equation finite difference method numerical simulation |
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