The spreading fronts in a mutualistic model with advection

Mei  Li; Zhigui Lin

doi:10.3934/dcdsb.2015.20.2089

Article Contents

2015, Volume 20, Issue 7: 2089-2105. Doi: 10.3934/dcdsb.2015.20.2089

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The spreading fronts in a mutualistic model with advection

Mei Li^1, and
Zhigui Lin^2,

1.
School of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210023
2.
School of Mathematical Science, Yangzhou University, Yangzhou 225002

Received: September 2014

Revised: March 2015

Published: September 2015

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Abstract

This paper is concerned with a system of semilinear parabolic equations with two free boundaries, which describe the spreading fronts of the invasive species in a mutualistic ecological model. The advection term is introduced to model the behavior of the invasive species in one dimension space. The local existence and uniqueness of a classical solution are obtained and the asymptotic behavior of the free boundary problem is studied. Our results indicate that for small advection, two free boundaries tend monotonically to finite limits or infinities at the same time, and a spreading-vanishing dichotomy holds, namely, either the expanding environment is limited and the invasive species dies out, or the invasive species spreads to all new environment and establishes itself in a long run. Moreover, some rough estimates of the spreading speed are also given when spreading happens.

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Mathematics Subject Classification: Primary: 35R35; Secondary: 35K60.

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