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100   $a20180525d2018      u|         0
101 0 $aeng
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181   $ctxt$2rdacontent
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200 10$aAsymptotics of Elliptic and Parabolic PDEs $eand their Applications in Statistical Physics, Computational Neuroscience, and Biophysics /$fby David Holcman, Zeev Schuss
205   $a1st ed. 2018.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2018.
215   $a1 online resource (XXIII, 444 p. 103 illus., 56 illus. in color.)
225 1 $aApplied Mathematical Sciences,$x0066-5452 ;$v199
311 08$a3-319-76894-8 
327   $aPart I. Singular Perturbations of Elliptic Boundary Problems -- 1 Second-Order Elliptic Boundary Value Problems with a Small Leading Part -- 2 A Primer of Asymptotics for ODEs -- 3 Singular Perturbations in Higher Dimensions -- 4 Eigenvalues of a Non-self-adjoint Elliptic Operator -- 5 Short-time Asymptotics of the Heat Kernel -- Part II Mixed Boundary Conditions for Elliptic and Parabolic Equations -- 6 The Mixed Boundary Value Problem -- 7 THe Mixed Boundary Value Problem in R2 -- 8 Narrow Escape in R3 -- 9 Short-time Asymptotics of the Heat Kernel and Extreme Statistics of the NET -- 10 The Poisson?Nernst?Planck Equations in a Ball -- 11 Reconstruction of Surface Diffusion from Projected Data -- 12 Asymptotic Formulas in Molecular and Cellular Biology -- Bibliography -- Index.
330   $aThis is a monograph on the emerging branch of mathematical biophysics combining asymptotic analysis with numerical and stochastic methods to analyze partial differential equations arising in biological and physical sciences. In more detail, the book presents the analytic methods and tools for approximating solutions of mixed boundary value problems, with particular emphasis on the narrow escape problem. Informed throughout by real-world applications, the book includes topics such as the Fokker-Planck equation, boundary layer analysis, WKB approximation, applications of spectral theory, as well as recent results in narrow escape theory. Numerical and stochastic aspects, including mean first passage time and extreme statistics, are discussed in detail and relevant applications are presented in parallel with the theory. Including background on the classical asymptotic theory of differential equations, this book is written for scientists of various backgrounds interested in deriving solutions to real-world problems from first principles.
410  0$aApplied Mathematical Sciences,$x0066-5452 ;$v199
606   $aDifferential equations, Partial
606   $aMathematical physics
606   $aPhysics
606   $aBiomathematics
606   $aBiophysics
606   $aBiophysics
606   $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155
606   $aMathematical Applications in the Physical Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/M13120
606   $aNumerical and Computational Physics, Simulation$3https://scigraph.springernature.com/ontologies/product-market-codes/P19021
606   $aMathematical and Computational Biology$3https://scigraph.springernature.com/ontologies/product-market-codes/M31000
606   $aMathematical Methods in Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19013
606   $aBiological and Medical Physics, Biophysics$3https://scigraph.springernature.com/ontologies/product-market-codes/P27008
615  0$aDifferential equations, Partial.
615  0$aMathematical physics.
615  0$aPhysics.
615  0$aBiomathematics.
615  0$aBiophysics.
615  0$aBiophysics.
615 14$aPartial Differential Equations.
615 24$aMathematical Applications in the Physical Sciences.
615 24$aNumerical and Computational Physics, Simulation.
615 24$aMathematical and Computational Biology.
615 24$aMathematical Methods in Physics.
615 24$aBiological and Medical Physics, Biophysics.
676   $a515.353
700   $aHolcman$b David$4aut$4http://id.loc.gov/vocabulary/relators/aut$0768213
702   $aSchuss$b Zeev$4aut$4http://id.loc.gov/vocabulary/relators/aut
906   $aBOOK
912   $a9910300108103321
996   $aAsymptotics of Elliptic and Parabolic PDEs$92018996
997   $aUNINA