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

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.

COMMUNICATED BY:

• Ming Mei

KEYWORDS:

• Reaction–advection–diffusion equation
• variable intrinsic growth rate
• Robin boundary condition
• free boundary problem
• spreading and vanishing

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 35K20
• 35R35
• 35B40

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].