Electron. J. Diff. Equ., Vol. 2015 (2015), No. 249, pp. 1-14.

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 grow-up 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; grow-up solution; global fast solution; global slow solution.

Show me the PDF file (237 KB), TEX file, and other files for this article.

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

Return to the EJDE web page