---
res:
bibo_abstract:
- "Mathematical models based on systems of reaction-diffusion equations provide
fundamental\r\ntools for the description and investigation of various processes
in biology, biochemistry, and chemistry;\r\nin specific situations, an appealing
characteristic of the arising nonlinear partial differential equations is\r\nthe
formation of patterns, reminiscent of those found in nature. The deterministic
Gray–Scott equations\r\nconstitute an elementary two-component system that describes
autocatalytic reaction processes; depending\r\non the choice of the specific parameters,
complex patterns of spirals, waves, stripes, or spots appear.\r\nIn the derivation
of a macroscopic model such as the deterministic Gray–Scott equations from basic
physical principles, certain aspects of microscopic dynamics, e.g. fluctuations
of molecules, are disregarded; an\r\nexpedient mathematical approach that accounts
for significant microscopic effects relies on the incorporation\r\nof stochastic
processes and the consideration of stochastic partial differential equations.\r\nThe
present work is concerned with a theoretical and numerical study of the stochastic
Gray–Scott\r\nequations driven by independent spatially time-homogeneous Wiener
processes. Under suitable regularity\r\nassumptions on the prescribed initial
states, existence and uniqueness of the solution processes is proven.\r\nNumerical
simulations based on the application of a time-adaptive first-order operator splitting
method and\r\nthe fast Fourier transform illustrate the formation of patterns
in the deterministic case and their variation\r\nunder the influence of stochastic
noise@eng"
bibo_authorlist:
- foaf_Person:
foaf_givenName: Erika
foaf_name: Hausenblas, Erika
foaf_surname: Hausenblas
- foaf_Person:
foaf_givenName: Tsiry Avisoa
foaf_name: Randrianasolo, Tsiry Avisoa
foaf_surname: Randrianasolo
foaf_workInfoHomepage: http://www.librecat.org/personId=114004016
orcid: 0000-0002-9413-5189
orcid_put_code_url: https://api.orcid.org/v2.0/0000-0002-9413-5189/work/54599394
- foaf_Person:
foaf_givenName: Mechthild
foaf_name: Thalhammer, Mechthild
foaf_surname: Thalhammer
bibo_doi: 10.1016/j.cam.2019.06.051
bibo_volume: 364
dct_date: 2019^xs_gYear
dct_identifier:
- UT:000488995800041
dct_isPartOf:
- http://id.crossref.org/issn/0377-0427
dct_language: eng
dct_publisher: Elsevier@
dct_subject:
- Mathematical and theoretical biology
- Mathematical biochemistry
- Mathematical chemistry
- Reaction-diffusion systems
- Gray–Scott equations
- Turing patterns
- Stochastic partial differential equations
- Wiener processes
- Numerical approximation
- Operator splitting methods
- Fast Fourier transform.
dct_title: Theoretical study and numerical simulation of pattern formation in the
deterministic and stochastic Gray--Scott equations@
...