Singular limit of reactiondiffusion systems and modified motion by mean curvature

2002 ◽  
Vol 132 (4) ◽  
pp. 951-973 ◽  
Author(s):  
E. Logak
Keyword(s):  
Mean Curvature ◽  
Diblock Copolymers ◽  
Free Boundary Problems ◽  
Reaction Diffusion ◽  
Magnetic Films ◽  
Boundary Problems ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Thin Magnetic Films ◽  
Motion By Mean Curvature

We consider two model reaction-diffusion systems of bistable type arising in the theory of phase transition; they appear in various physical contexts, such as thin magnetic films and diblock copolymers. We prove the convergence of the solution of these systems to the solution of free-boundary problems involving modified motion by mean curvature.

scholarly journals Highly scalable numerical simulation of coupled reaction–Diffusion systems with moving interfaces

2021 ◽  
pp. 109434202110459
Author(s):  
Mojtaba Barzegari ◽  
Liesbet Geris
Keyword(s):  
High Performance ◽  
Moving Boundary ◽  
Reaction Diffusion ◽  
Diffusion Reaction ◽  
Boundary Problems ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Wide Range ◽  
Strong Scaling ◽  
Reaction Processes

A combination of reaction–diffusion models with moving-boundary problems yields a system in which the diffusion (spreading and penetration) and reaction (transformation) evolve the system’s state and geometry over time. These systems can be used in a wide range of engineering applications. In this study, as an example of such a system, the degradation of metallic materials is investigated. A mathematical model is constructed of the diffusion-reaction processes and the movement of corrosion front of a magnesium block floating in a chemical solution. The corresponding parallelized computational model is implemented using the finite element method, and the weak and strong-scaling behaviors of the model are evaluated to analyze the performance and efficiency of the employed high-performance computing techniques.

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>

scholarly journals Wavelength Selection by Interrupted Coarsening in Reaction-Diffusion Systems

2021 ◽  
Vol 126 (10) ◽  
Author(s):  
Fridtjof Brauns ◽  
Henrik Weyer ◽  
Jacob Halatek ◽  
Junghoon Yoon ◽  
Erwin Frey
Keyword(s):  
Reaction Diffusion ◽  
Wavelength Selection ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems
Sign in / Sign up

Export Citation Format

Share Document