Exhibiting cross-diffusion-induced patterns for reaction-diffusion systems on evolving domains and surfaces
نویسندگان
چکیده
منابع مشابه
Exhibiting cross-diffusion-induced patterns for reaction-diffusion systems on evolving domains and surfaces.
The aim of this manuscript is to present for the first time the application of the finite element method for solving reaction-diffusion systems with cross-diffusion on continuously evolving domains and surfaces. Furthermore we present pattern formation generated by the reaction-diffusion system with cross-diffusion on evolving domains and surfaces. A two-component reaction-diffusion system with...
متن کاملGlobal existence for semilinear reaction-diffusion systems on evolving domains.
We present global existence results for solutions of reaction-diffusion systems on evolving domains. Global existence results for a class of reaction-diffusion systems on fixed domains are extended to the same systems posed on spatially linear isotropically evolving domains. The results hold without any assumptions on the sign of the growth rate. The analysis is valid for many systems that comm...
متن کاملStability analysis of reaction-diffusion models on evolving domains: the effects of cross-diffusion
This article presents stability analytical results of a two component reaction-diffusion system with linear cross-diffusion posed on continuously evolving domains. First the model system is mapped from a continuously evolving domain to a reference stationary frame resulting in a system of partial differential equations with time-dependent coefficients. Second, by employing appropriately asympto...
متن کاملCross-diffusion Induced Instability and Stability in Reaction-diffusion Systems
In a reaction-diffusion system, diffusion can induce the instability of a uniform equilibrium which is stable with respect to a constant perturbation, as shown by Turing in 1950s. We show that cross-diffusion can destabilize a uniform equilibrium which is stable for the kinetic and self-diffusion reaction systems; on the other hand, cross-diffusion can also stabilize a uniform equilibrium which...
متن کاملEvolving Reaction-Diffusion Systems on GPU
Reaction-diffusion systems contribute to various morphogenetic processes, and can also be used as computation models in real and artificial chemistries. Evolving reaction-diffusion solutions automatically is interesting because it is otherwise difficult to engineer them to achieve a target pattern or to perform a desired task. However most of the existing work focuses on the optimization of par...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Physical Review E
سال: 2014
ISSN: 1539-3755,1550-2376
DOI: 10.1103/physreve.90.043307