TY - JOUR
T1 - On a free boundary problem for a reaction–diffusion–advection logistic model in heterogeneous environment
AU - Monobe, Harunori
AU - Wu, Chang Hong
N1 - Funding Information:
The authors are grateful to two anonymous referees for their helpful comments and suggestions which strengthen the paper. CHW is partly supported by the Ministry of Science and Technology of Taiwan under the MOST 104-2115-M-024-001 . CHW thanks Professor Yihong Du and Professor Yuan Lou for some useful suggestions.
Publisher Copyright:
© 2016 Elsevier Inc.
PY - 2016/12/5
Y1 - 2016/12/5
N2 - In this paper, we investigate a reaction–diffusion–advection equation with a free boundary which models the spreading of an invasive species in one-dimensional heterogeneous environments. We assume that the species has a tendency to move upward along the resource gradient in addition to random dispersal, and the spreading mechanism of species is determined by a Stefan-type condition. Investigating the sign of the principal eigenvalue of the associated linearized eigenvalue problem, under certain conditions we obtain the sharp criteria for spreading and vanishing via system parameters. Also, we establish the long-time behavior of the solution and the asymptotic spreading speed. Finally, some biological implications are discussed.
AB - In this paper, we investigate a reaction–diffusion–advection equation with a free boundary which models the spreading of an invasive species in one-dimensional heterogeneous environments. We assume that the species has a tendency to move upward along the resource gradient in addition to random dispersal, and the spreading mechanism of species is determined by a Stefan-type condition. Investigating the sign of the principal eigenvalue of the associated linearized eigenvalue problem, under certain conditions we obtain the sharp criteria for spreading and vanishing via system parameters. Also, we establish the long-time behavior of the solution and the asymptotic spreading speed. Finally, some biological implications are discussed.
KW - Free boundary problem
KW - Heterogeneous environments
KW - Population dynamics
KW - Reaction–diffusion–advection equation
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U2 - 10.1016/j.jde.2016.08.033
DO - 10.1016/j.jde.2016.08.033
M3 - Article
AN - SCOPUS:84994481752
VL - 261
SP - 6144
EP - 6177
JO - Journal of Differential Equations
JF - Journal of Differential Equations
SN - 0022-0396
IS - 11
ER -