We investigate a reaction--diffusion system proposed by H. Meinhardt
as a model for pattern formation on seashells. We give a new proof
for the existence of a local weak solution for general initial conditions
and parameters upon using an iterative approach. Furthermore, the
solution is shown to exist globally for suitable initial data. The
behavior of the solution in time and space is illustrated through
numerical simulations. Copyright � 2009 John Wiley & Sons, Ltd.
%0 Journal Article
%1 kelkel2009solution
%A Kelkel, Jan
%A Surulescu, Christina
%D 2009
%I John Wiley & Sons, Ltd.
%J Mathematical Methods in the Applied Sciences
%K equations, formation, from:mhartmann global ians pattern reaction--diffusion solution vorlaeufig weak
%N 17
%P 2267--2286
%R 10.1002/mma.1133
%T A weak solution approach to a reaction--diffusion system modeling
pattern formation on seashells
%U http://dx.doi.org/10.1002/mma.1133
%V 32
%X We investigate a reaction--diffusion system proposed by H. Meinhardt
as a model for pattern formation on seashells. We give a new proof
for the existence of a local weak solution for general initial conditions
and parameters upon using an iterative approach. Furthermore, the
solution is shown to exist globally for suitable initial data. The
behavior of the solution in time and space is illustrated through
numerical simulations. Copyright � 2009 John Wiley & Sons, Ltd.
@article{kelkel2009solution,
abstract = {We investigate a reaction--diffusion system proposed by H. Meinhardt
as a model for pattern formation on seashells. We give a new proof
for the existence of a local weak solution for general initial conditions
and parameters upon using an iterative approach. Furthermore, the
solution is shown to exist globally for suitable initial data. The
behavior of the solution in time and space is illustrated through
numerical simulations. Copyright � 2009 John Wiley \& Sons, Ltd.},
added-at = {2018-07-20T10:54:47.000+0200},
author = {Kelkel, Jan and Surulescu, Christina},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/21012825ed1ef9d03d4f860e87a435b62/mathematik},
doi = {10.1002/mma.1133},
interhash = {238011336a3e7e95eec6ac89a22367c8},
intrahash = {1012825ed1ef9d03d4f860e87a435b62},
issn = {1099-1476},
journal = {Mathematical Methods in the Applied Sciences},
keywords = {equations, formation, from:mhartmann global ians pattern reaction--diffusion solution vorlaeufig weak},
number = 17,
pages = {2267--2286},
publisher = {John Wiley \& Sons, Ltd.},
timestamp = {2019-12-18T14:37:55.000+0100},
title = {A weak solution approach to a reaction--diffusion system modeling
pattern formation on seashells},
url = {http://dx.doi.org/10.1002/mma.1133},
volume = 32,
year = 2009
}
