000 04343nam a22006015i 4500
001 978-3-319-67944-0
003 DE-He213
005 20220801214924.0
007 cr nn 008mamaa
008 171128s2018 sz | s |||| 0|eng d
020 _a9783319679440
_9978-3-319-67944-0
024 7 _a10.1007/978-3-319-67944-0
_2doi
050 4 _aTA349-359
072 7 _aTGB
_2bicssc
072 7 _aTEC009070
_2bisacsh
072 7 _aTGB
_2thema
082 0 4 _a620.1
_223
100 1 _aKavallaris, Nikos I.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_941264
245 1 0 _aNon-Local Partial Differential Equations for Engineering and Biology
_h[electronic resource] :
_bMathematical Modeling and Analysis /
_cby Nikos I. Kavallaris, Takashi Suzuki.
250 _a1st ed. 2018.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2018.
300 _aXIX, 300 p. 23 illus., 7 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aMathematics for Industry,
_x2198-3518 ;
_v31
505 0 _aDedication -- Preface -- Acknowledgements -- Part I Applications in Engineering -- Micro-electro-mechanical-systems(MEMS) -- Ohmic Heating Phenomena -- Linear Friction Welding -- Resistance Spot Welding -- Part II Applications in Biology -- Gierer-Meinhardt System -- A Non-local Model Illustrating Replicator Dynamics -- A Non-local Model Arising in Chemotaxis -- A Non-local Reaction-Diffusion System Illustrating Cell Dynamics -- Appendices -- Index.
520 _aThis book presents new developments in non-local mathematical modeling and mathematical analysis on the behavior of solutions with novel technical tools. Theoretical backgrounds in mechanics, thermo-dynamics, game theory, and theoretical biology are examined in details. It starts off with a review and summary of the basic ideas of mathematical modeling frequently used in the sciences and engineering. The authors then employ a number of models in bio-science and material science to demonstrate applications, and provide recent advanced studies, both on deterministic non-local partial differential equations and on some of their stochastic counterparts used in engineering. Mathematical models applied in engineering, chemistry, and biology are subject to conservation laws. For instance, decrease or increase in thermodynamic quantities and non-local partial differential equations, associated with the conserved physical quantities as parameters. These present novel mathematical objects are engaged with rich mathematical structures, in accordance with the interactions between species or individuals, self-organization, pattern formation, hysteresis. These models are based on various laws of physics, such as mechanics of continuum, electro-magnetic theory, and thermodynamics. This is why many areas of mathematics, calculus of variation, dynamical systems, integrable systems, blow-up analysis, and energy methods are indispensable in understanding and analyzing these phenomena. This book aims for researchers and upper grade students in mathematics, engineering, physics, economics, and biology.
650 0 _aMechanics, Applied.
_93253
650 0 _aMathematical physics.
_911013
650 0 _aBioinformatics.
_99561
650 0 _aDifferential equations.
_941265
650 0 _aChemistry, Technical.
_914638
650 1 4 _aEngineering Mechanics.
_931830
650 2 4 _aMathematical Physics.
_911013
650 2 4 _aComputational and Systems Biology.
_931619
650 2 4 _aDifferential Equations.
_941266
650 2 4 _aIndustrial Chemistry.
_914640
700 1 _aSuzuki, Takashi.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_941267
710 2 _aSpringerLink (Online service)
_941268
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783319679426
776 0 8 _iPrinted edition:
_z9783319679433
776 0 8 _iPrinted edition:
_z9783319885155
830 0 _aMathematics for Industry,
_x2198-3518 ;
_v31
_941269
856 4 0 _uhttps://doi.org/10.1007/978-3-319-67944-0
912 _aZDB-2-ENG
912 _aZDB-2-SXE
942 _cEBK
999 _c76905
_d76905