國立虎尾科技大學 |

Asymptotics of elliptic and parabolic PDEs = and their applications in statistical physics, computational neuroscience, and biophysics /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Asymptotics of elliptic and parabolic PDEs/ by David Holcman, Zeev Schuss.
其他題名:	and their applications in statistical physics, computational neuroscience, and biophysics /
作者:	Holcman, David.
其他作者:	Schuss, Zeev.
出版者:	Cham :Springer International Publishing : : 2018.,
面頁冊數:	xxiii, 444 p. :ill. (some col.), digital ; : 24 cm.;
Contained By:	Springer eBooks
標題:	Differential equations, Elliptic - Asymptotic theory. -
電子資源:	http://dx.doi.org/10.1007/978-3-319-76895-3
ISBN:	9783319768953

Asymptotics of elliptic and parabolic PDEs = and their applications in statistical physics, computational neuroscience, and biophysics /
Holcman, David.

Asymptotics of elliptic and parabolic PDEsand their applications in statistical physics, computational neuroscience, and biophysics /[electronic resource] :by David Holcman, Zeev Schuss. - Cham :Springer International Publishing :2018. - xxiii, 444 p. :ill. (some col.), digital ;24 cm. - Applied mathematical sciences,v.1990066-5452 ;. - Applied mathematical sciences ;v.173..

Part 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.

This 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.

ISBN: 9783319768953

Standard No.: 10.1007/978-3-319-76895-3doiSubjects--Topical Terms:

1205159
Differential equations, Elliptic
--Asymptotic theory.

LC Class. No.: QA377 / .H653 2018

Dewey Class. No.: 515.3533

Asymptotics of elliptic and parabolic PDEs = and their applications in statistical physics, computational neuroscience, and biophysics /
LDR:02959nam a2200325 a 4500 001 926551
003 DE-He213
005 20181130104325.0
006 m d
007 cr nn 008maaau
008 190625s2018 gw s 0 eng d
020 $a 9783319768953 $q (electronic bk.)
020 $a 9783319768946 $q (paper)
024 7 $a 10.1007/978-3-319-76895-3 $2 doi
035 $a 978-3-319-76895-3
040 $a GP $c GP
041 0 $a eng
050 4 $a QA377 $b .H653 2018
072 7 $a PBKJ $2 bicssc
072 7 $a MAT007000 $2 bisacsh
082 0 4 $a 515.3533 $2 23
090 $a QA377 $b .H725 2018
100 1 $a Holcman, David. $3 1070127
245 1 0 $a Asymptotics of elliptic and parabolic PDEs $h [electronic resource] : $b and their applications in statistical physics, computational neuroscience, and biophysics / $c by David Holcman, Zeev Schuss.
260 $a Cham : $c 2018. $b Springer International Publishing : $b Imprint: Springer,
300 $a xxiii, 444 p. : $b ill. (some col.), digital ; $c 24 cm.
490 1 $a Applied mathematical sciences, $x 0066-5452 ; $v v.199
505 0 $a Part 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.
520 $a This 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.
650 0 $a Differential equations, Elliptic $x Asymptotic theory. $3 1205159
650 0 $a Differential equations, Partial $x Asymptotic theory. $3 672312
650 1 4 $a Mathematics. $3 527692
650 2 4 $a Partial Differential Equations. $3 671119
650 2 4 $a Mathematical Applications in the Physical Sciences. $3 786649
650 2 4 $a Numerical and Computational Physics, Simulation. $3 1112293
650 2 4 $a Mathematical and Computational Biology. $3 786706
650 2 4 $a Mathematical Methods in Physics. $3 670749
650 2 4 $a Biological and Medical Physics, Biophysics. $3 1113305
700 1 $a Schuss, Zeev. $3 888930
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer eBooks
830 0 $a Applied mathematical sciences ; $v v.173. $3 881311
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-76895-3
950 $a Mathematics and Statistics (Springer-11649)