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001 978-1-4471-5526-3
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008 130918s2014 xxk| s |||| 0|eng d
020 _a9781447155263
_9978-1-4471-5526-3
024 7 _a10.1007/978-1-4471-5526-3
_2doi
050 4 _aQA370-380
072 7 _aPBKJ
_2bicssc
072 7 _aMAT007000
_2bisacsh
082 0 4 _a515.353
_223
100 1 _aWei, Juncheng.
_eauthor.
245 1 0 _aMathematical Aspects of Pattern Formation in Biological Systems
_h[electronic resource] /
_cby Juncheng Wei, Matthias Winter.
264 1 _aLondon :
_bSpringer London :
_bImprint: Springer,
_c2014.
300 _aXII, 319 p. 20 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aApplied Mathematical Sciences,
_x0066-5452 ;
_v189
505 0 _aIntroduction -- Existence of spikes for the Gierer-Meinhardt system in one dimension -- The Nonlocal Eigenvalue Problem (NLEP) -- Stability of spikes for the Gierer-Meinhardt system in one dimension -- Existence of spikes for the shadow Gierer-Meinhardt system -- Existence and stability of spikes for the Gierer-Meinhardt system in two dimensions -- The Gierer-Meinhardt system with inhomogeneous coefficients -- Other aspects of the Gierer-Meinhardt system -- The Gierer-Meinhardt system with saturation -- Spikes for other two-component reaction-diffusion systems -- Reaction-diffusion systems with many components -- Biological applications -- Appendix.
520 _aThis monograph is concerned with the mathematical analysis of patterns which are encountered in biological systems. It summarises, expands and relates results obtained in the field during the last fifteen years. It also links the results to biological applications and highlights their relevance to phenomena in nature. Of particular concern are large-amplitude patterns far from equilibrium in biologically relevant models. The approach adopted in the monograph is based on the following paradigms: • Examine the existence of spiky steady states in reaction-diffusion systems and select as observable patterns only the stable ones • Begin by exploring spatially homogeneous two-component activator-inhibitor systems in one or two space dimensions • Extend the studies by considering extra effects or related systems, each motivated by their specific roles in developmental biology, such as spatial inhomogeneities, large reaction rates, altered boundary conditions, saturation terms, convection, many-component systems. Mathematical Aspects of Pattern Formation in Biological Systems will be of interest to graduate students and researchers who are active in reaction-diffusion systems, pattern formation and mathematical biology.
650 0 _aMathematics.
650 0 _aDifferential equations, partial.
650 0 _aGenetics
_xMathematics.
650 0 _aPhysiology
_xMathematics.
650 1 4 _aMathematics.
650 2 4 _aPartial Differential Equations.
650 2 4 _aMathematical and Computational Biology.
650 2 4 _aGenetics and Population Dynamics.
650 2 4 _aPhysiological, Cellular and Medical Topics.
700 1 _aWinter, Matthias.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781447155256
830 0 _aApplied Mathematical Sciences,
_x0066-5452 ;
_v189
856 4 0 _uhttp://dx.doi.org/10.1007/978-1-4471-5526-3
912 _aZDB-2-SMA
999 _c91902
_d91902