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Applicable Analysis
An International Journal
Volume 99, 2020 - Issue 8
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Articles

On a reaction–advection–diffusion equation with Robin and free boundary conditions

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Pages 1344-1358 | Received 31 Mar 2018, Accepted 23 Sep 2018, Published online: 12 Oct 2018
 

ABSTRACT

A reaction–advection–diffusion equation with variable intrinsic growth rate, Robin and free boundary conditions is investigated in this paper. Firstly, we present a spreading–vanishing dichotomy for the asymptotic behavior of the solutions of the equation. Then, we obtain criteria for spreading and vanishing, and get an estimate for the asymptotic spreading speed of the spreading front. Moreover, numerical simulation is also given to illustrate the impact of the expansion capacity on the free boundary.

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Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 11771407]; the Innovative Research Team of Science and Technology in Henan Province [grant number 17IRTSTHN007]; and the National Key R&D Program of China [grant number 2017YFB0702500].

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