Electron. J. Diff. Equ.,
Vol. 2015 (2015), No. 249, pp. 114.
Existence of global solutions to a mutualistic model with double fronts
Mei Li, Lin Lin
Abstract:
We study a system of semilinear parabolic equations with two free boundaries
describing the spreading fronts of the invasive species in a mutualistic
ecological model. We establish the existence and uniqueness of a local
classical solution and then study the asymptotic behavior of the free boundary
problem. The results indicate that two free boundaries tend monotonically to
finite values at the same time, or to infinite simultaneously. Also
the free boundary problem admits a global slow solution with unbounded
free boundaries if the geometric average of the interaction coefficients
is less than 1, while if it is bigger than 1 there exist the growup
solution and global fast solution with bounded free boundaries.
Submitted December 14, 2014. Published September 25, 2015.
Math Subject Classifications: 35R35, 35K60.
Key Words: Mutualistic model; free boundary; growup solution;
global fast solution; global slow solution.
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Mei Li
School of Mathematical Science
Nanjing Normal University
Nanjing 210023, China
email: limei@njue.edu.cn


Lin Lin
School of Mathematical Science
Nanjing Normal University
Nanjing 210023, China
email: linlin@njnu.edu.cn

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