Abstract
This paper deals with a free boundary problem for diffusion equation with a certain class of bistable nonlinearity which allows two positive stable equilibrium states as an ODE model. This problem models the invasion of a biological species and the free boundary represents the spreading front of its habitat. Our main interest is to study large-time behaviors of solutions for the free boundary problem. We will completely classify asymptotic behaviors of solutions and, in particular, observe two different types of spreading phenomena corresponding to two positive stable equilibrium states. Moreover, it will be proved that, if the free boundary expands to infinity, an asymptotic speed of the moving free boundary for large time can be uniquely determined from the related semi-wave problem.
| Original language | English |
|---|---|
| Pages (from-to) | 538-572 |
| Number of pages | 35 |
| Journal | Journal of Differential Equations |
| Volume | 261 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2016 Jul 5 |
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Keywords
- Comparison theorem
- Free boundary problem
- Reaction-diffusion equation
- Semi-wave
- Spreading
- Vanishing
ASJC Scopus subject areas
- Analysis
Cite this
Multiple spreading phenomena for a free boundary problem of a reaction-diffusion equation with a certain class of bistable nonlinearity. / Kawai, Yusuke; Yamada, Yoshio.
In: Journal of Differential Equations, Vol. 261, No. 1, 05.07.2016, p. 538-572.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Multiple spreading phenomena for a free boundary problem of a reaction-diffusion equation with a certain class of bistable nonlinearity
AU - Kawai, Yusuke
AU - Yamada, Yoshio
PY - 2016/7/5
Y1 - 2016/7/5
N2 - This paper deals with a free boundary problem for diffusion equation with a certain class of bistable nonlinearity which allows two positive stable equilibrium states as an ODE model. This problem models the invasion of a biological species and the free boundary represents the spreading front of its habitat. Our main interest is to study large-time behaviors of solutions for the free boundary problem. We will completely classify asymptotic behaviors of solutions and, in particular, observe two different types of spreading phenomena corresponding to two positive stable equilibrium states. Moreover, it will be proved that, if the free boundary expands to infinity, an asymptotic speed of the moving free boundary for large time can be uniquely determined from the related semi-wave problem.
AB - This paper deals with a free boundary problem for diffusion equation with a certain class of bistable nonlinearity which allows two positive stable equilibrium states as an ODE model. This problem models the invasion of a biological species and the free boundary represents the spreading front of its habitat. Our main interest is to study large-time behaviors of solutions for the free boundary problem. We will completely classify asymptotic behaviors of solutions and, in particular, observe two different types of spreading phenomena corresponding to two positive stable equilibrium states. Moreover, it will be proved that, if the free boundary expands to infinity, an asymptotic speed of the moving free boundary for large time can be uniquely determined from the related semi-wave problem.
KW - Comparison theorem
KW - Free boundary problem
KW - Reaction-diffusion equation
KW - Semi-wave
KW - Spreading
KW - Vanishing
UR - http://www.scopus.com/inward/record.url?scp=84961837637&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84961837637&partnerID=8YFLogxK
U2 - 10.1016/j.jde.2016.03.017
DO - 10.1016/j.jde.2016.03.017
M3 - Article
VL - 261
SP - 538
EP - 572
JO - Journal of Differential Equations
JF - Journal of Differential Equations
SN - 0022-0396
IS - 1
ER -