Zobrazeno 1 - 10
of 654
pro vyhledávání: '"Marciniak-Czochra A"'
This paper presents a mathematical framework for modeling the dynamics of heterogeneous populations. Models describing local and non-local growth and transport processes, dependent on dynamically changing population structures, appear in a variety of
Externí odkaz:
http://arxiv.org/abs/2307.10957
Autor:
Qin Pan, Moritz Mercker, Alexander Klimovich, Jörg Wittlieb, Anna Marciniak-Czochra, Angelika Böttger
Publikováno v:
Scientific Reports, Vol 14, Iss 1, Pp 1-16 (2024)
Abstract The Notch-signalling pathway plays an important role in pattern formation in Hydra. Using pharmacological Notch inhibitors (DAPT and SAHM1), it has been demonstrated that HvNotch is required for head regeneration and tentacle patterning in H
Externí odkaz:
https://doaj.org/article/a11ea9e31c7441e98a306ca4a52fed3c
We derive a macroscopic limit for a sharp interface version of a model proposed in [29] to investigate pattern formation due to competition of chemical and mechanical forces in biomembranes. We identify sub- and supercrital parameter regimes and show
Externí odkaz:
http://arxiv.org/abs/2207.01974
Systems consisting of a single ordinary differential equation coupled with one reaction-diffusion equation in a bounded domain and with the Neumann boundary conditions are studied in the case of particular nonlinearities from the Brusselator model, t
Externí odkaz:
http://arxiv.org/abs/2206.15161
Pattern formation in biological tissues plays an important role in the development of living organisms. Since the classical work of Alan Turing, a pre-eminent way of modelling has been through reaction-diffusion mechanisms. More recently, alternative
Externí odkaz:
http://arxiv.org/abs/2203.14742
Reaction-diffusion equations coupled to ordinary differential equations (ODEs) may exhibit spatially low-regular stationary solutions. This work provides a comprehensive theory of asymptotic stability of bounded, discontinuous or continuous, stationa
Externí odkaz:
http://arxiv.org/abs/2201.12748
A general system of n ordinary differential equations coupled with one reaction-diffusion equation, considered in a bounded N-dimensional domain, with no-flux boundary condition is studied in a context of pattern formation. Such initial boundary valu
Externí odkaz:
http://arxiv.org/abs/2111.01214
Shadow systems are an approximation of reaction-diffusion-type problems obtained in the infinite diffusion coefficient limit. They allow reducing complexity of the system and hence facilitate its analysis. The quality of approximation can be consider
Externí odkaz:
http://arxiv.org/abs/2110.06745
We obtain an existence result for a Measure Differential Equation with an additional nonlinear growth/decay term that may change the sign. The proof requires a modification of approximating schemes proposed by Piccoli and Rossi. The new scheme combin
Externí odkaz:
http://arxiv.org/abs/2109.14987
A general system of several ordinary differential equations coupled with a reaction-diffusion equation in a bounded domain with zero-flux boundary condition is studied in the context of pattern formation. These initial-boundary value problems may hav
Externí odkaz:
http://arxiv.org/abs/2105.05023