TY - JOUR
T1 - Spreading and vanishing behaviors for radially symmetric solutions of free boundary problems for reaction-diffusion equations
AU - Kaneko, Yuki
PY - 2014
Y1 - 2014
N2 - We discuss free boundary problems modeling the diffusion of invasive or new species in a multi-dimensional ball or annulus, where unknown functions are population density and the outer boundary representing the spreading front of the species. We define spreading and vanishing to describe the asymptotic behaviors of radially symmetric solutions. The main purpose is to study the underlying principle to determine spreading and vanishing for the free boundary problems of general reaction-diffusion equations. We also focus on the problems with a logistic or bistable reaction term to show dichotomy results, vanishing speed and sufficient conditions for spreading or vanishing.
AB - We discuss free boundary problems modeling the diffusion of invasive or new species in a multi-dimensional ball or annulus, where unknown functions are population density and the outer boundary representing the spreading front of the species. We define spreading and vanishing to describe the asymptotic behaviors of radially symmetric solutions. The main purpose is to study the underlying principle to determine spreading and vanishing for the free boundary problems of general reaction-diffusion equations. We also focus on the problems with a logistic or bistable reaction term to show dichotomy results, vanishing speed and sufficient conditions for spreading or vanishing.
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U2 - 10.1016/j.nonrwa.2014.01.008
DO - 10.1016/j.nonrwa.2014.01.008
M3 - Article
AN - SCOPUS:84897983938
VL - 18
SP - 121
EP - 140
JO - Nonlinear Analysis: Real World Applications
JF - Nonlinear Analysis: Real World Applications
SN - 1468-1218
IS - 1
ER -