Multiple Solutions in Reaction-Diffusion Systems with a Free Boundary

1989 ◽  
Vol 49 (1) ◽  
pp. 134-151 ◽  
Author(s):  
F. Conrad ◽  
N. Yebari
Keyword(s):  
Free Boundary ◽  
Multiple Solutions ◽  
Reaction Diffusion ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems

scholarly journals Lie symmetries and multiple solutions in reaction-diffusion systems

1997 ◽  
Vol 30 (1) ◽  
pp. 185-194 ◽  
Author(s):  
J F R Archilla ◽  
J L Romero ◽  
F Romero Romero ◽  
F Palmero
Keyword(s):  
Multiple Solutions ◽  
Reaction Diffusion ◽  
Lie Symmetries ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems

scholarly journals Two species nonlocal diffusion systems with free boundaries

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yihong Du ◽  
Mingxin Wang ◽  
Meng Zhao
Keyword(s):  
Free Boundary ◽  
Free Boundary Problems ◽  
Reaction Diffusion ◽  
Single Species ◽  
Diffusion Problem ◽  
Nonlocal Diffusion ◽  
Free Boundaries ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Local Diffusion

<p style='text-indent:20px;'>We study a class of free boundary systems with nonlocal diffusion, which are natural extensions of the corresponding free boundary problems of reaction diffusion systems. As before the free boundary represents the spreading front of the species, but here the population dispersal is described by "nonlocal diffusion" instead of "local diffusion". We prove that such a nonlocal diffusion problem with free boundary has a unique global solution, and for models with Lotka-Volterra type competition or predator-prey growth terms, we show that a spreading-vanishing dichotomy holds, and obtain criteria for spreading and vanishing; moreover, for the weak competition case and for the weak predation case, we can determine the long-time asymptotic limit of the solution when spreading happens. Compared with the single species free boundary model with nonlocal diffusion considered recently in [<xref ref-type="bibr" rid="b7">7</xref>], and the two species cases with local diffusion extensively studied in the literature, the situation considered in this paper involves several new difficulties, which are overcome by the use of some new techniques.</p>

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