東華大學圖書館 |

語系: 繁體中文

說明(常見問題)

回圖書館首頁

手機版館藏查詢

登入

回首頁 到查詢結果 [ subject:"Heat equation." ]

切換: 標籤 | MARC模式 | ISBD

Linear fractional diffusion-wave equ...

Povstenko, Yuriy.

FindBook

Google Book

Amazon

博客來

Linear fractional diffusion-wave equation for scientists and engineers

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Linear fractional diffusion-wave equation for scientists and engineers/ by Yuriy Povstenko.
作者:	Povstenko, Yuriy.
出版者:	Cham :Springer International Publishing : : 2015.,
面頁冊數:	xiv, 460 p. :ill. (some col.), digital ;24 cm.
內容註:	1.Introduction -- 2.Mathematical Preliminaries -- 3.Physical Backgrounds -- 4.Equations with one Space Variable in Cartesian Coordinates -- 5.Equations with one Space Variable in Polar Coordinates -- 6.Equations with one Space Variable in Spherical Coordinates -- 7.Equations with two Space Variables in Cartesian Coordinates -- 8.Equations in Polar Coordinates -- 9.Axisymmetric equations in Cylindrical Coordinates -- 10.Equations with three Space Variables in Cartesian Coordinates -- 11.Equations with three space Variables in Cylindrical Coordinates -- 12.Equations with three space Variables in Spherical Coordinates -- Conclusions -- Appendix: Integrals -- References.
Contained By:	Springer eBooks
標題:	Heat equation. -
電子資源:	http://dx.doi.org/10.1007/978-3-319-17954-4
ISBN:	9783319179544 (electronic bk.)

Linear fractional diffusion-wave equation for scientists and engineers
Povstenko, Yuriy.

Linear fractional diffusion-wave equation for scientists and engineers[electronic resource] /by Yuriy Povstenko. - Cham :Springer International Publishing :2015. - xiv, 460 p. :ill. (some col.), digital ;24 cm.

1.Introduction -- 2.Mathematical Preliminaries -- 3.Physical Backgrounds -- 4.Equations with one Space Variable in Cartesian Coordinates -- 5.Equations with one Space Variable in Polar Coordinates -- 6.Equations with one Space Variable in Spherical Coordinates -- 7.Equations with two Space Variables in Cartesian Coordinates -- 8.Equations in Polar Coordinates -- 9.Axisymmetric equations in Cylindrical Coordinates -- 10.Equations with three Space Variables in Cartesian Coordinates -- 11.Equations with three space Variables in Cylindrical Coordinates -- 12.Equations with three space Variables in Spherical Coordinates -- Conclusions -- Appendix: Integrals -- References.

This book systematically presents solutions to the linear time-fractional diffusion-wave equation. It introduces the integral transform technique and discusses the properties of the Mittag-Leffler, Wright, and Mainardi functions that appear in the solutions. The time-nonlocal dependence between the flux and the gradient of the transported quantity with the "long-tail" power kernel results in the time-fractional diffusion-wave equation with the Caputo fractional derivative. Time-nonlocal generalizations of classical Fourier's, Fick's and Darcy's laws are considered and different kinds of boundary conditions for this equation are discussed (Dirichlet, Neumann, Robin, perfect contact) The book provides solutions to the fractional diffusion-wave equation with one, two and three space variables in Cartesian, cylindrical and spherical coordinates. The respective sections of the book can be used for university courses on fractional calculus, heat and mass transfer, transport processes in porous media and fractals for graduate and postgraduate students. The volume will also serve as a valuable reference guide for specialists working in applied mathematics, physics, geophysics and the engineering sciences.

ISBN: 9783319179544 (electronic bk.)

Standard No.: 10.1007/978-3-319-17954-4doiSubjects--Topical Terms:

589024
Heat equation.

LC Class. No.: QA377

Dewey Class. No.: 515.353

Linear fractional diffusion-wave equation for scientists and engineers
LDR:02851nmm a2200313 a 4500 001 2009098
003 DE-He213
005 20160223113013.0
006 m d
007 cr nn 008maaau
008 160311s2015 gw s 0 eng d
020 $a 9783319179544 (electronic bk.)
020 $a 9783319179537 (paper)
024 7 $a 10.1007/978-3-319-17954-4 $2 doi
035 $a 978-3-319-17954-4
040 $a GP $c GP
041 0 $a eng
050 4 $a QA377
072 7 $a PBKJ $2 bicssc
072 7 $a MAT007000 $2 bisacsh
082 0 4 $a 515.353 $2 23
090 $a QA377 $b .P879 2015
100 1 $a Povstenko, Yuriy. $3 2134680
245 1 0 $a Linear fractional diffusion-wave equation for scientists and engineers $h [electronic resource] / $c by Yuriy Povstenko.
260 $a Cham : $b Springer International Publishing : $b Imprint: Birkhauser, $c 2015.
300 $a xiv, 460 p. : $b ill. (some col.), digital ; $c 24 cm.
505 0 $a 1.Introduction -- 2.Mathematical Preliminaries -- 3.Physical Backgrounds -- 4.Equations with one Space Variable in Cartesian Coordinates -- 5.Equations with one Space Variable in Polar Coordinates -- 6.Equations with one Space Variable in Spherical Coordinates -- 7.Equations with two Space Variables in Cartesian Coordinates -- 8.Equations in Polar Coordinates -- 9.Axisymmetric equations in Cylindrical Coordinates -- 10.Equations with three Space Variables in Cartesian Coordinates -- 11.Equations with three space Variables in Cylindrical Coordinates -- 12.Equations with three space Variables in Spherical Coordinates -- Conclusions -- Appendix: Integrals -- References.
520 $a This book systematically presents solutions to the linear time-fractional diffusion-wave equation. It introduces the integral transform technique and discusses the properties of the Mittag-Leffler, Wright, and Mainardi functions that appear in the solutions. The time-nonlocal dependence between the flux and the gradient of the transported quantity with the "long-tail" power kernel results in the time-fractional diffusion-wave equation with the Caputo fractional derivative. Time-nonlocal generalizations of classical Fourier's, Fick's and Darcy's laws are considered and different kinds of boundary conditions for this equation are discussed (Dirichlet, Neumann, Robin, perfect contact) The book provides solutions to the fractional diffusion-wave equation with one, two and three space variables in Cartesian, cylindrical and spherical coordinates. The respective sections of the book can be used for university courses on fractional calculus, heat and mass transfer, transport processes in porous media and fractals for graduate and postgraduate students. The volume will also serve as a valuable reference guide for specialists working in applied mathematics, physics, geophysics and the engineering sciences.
650 0 $a Heat equation. $3 589024
650 0 $a Mathematical physics. $3 516853
650 1 4 $a Mathematics. $3 515831
650 2 4 $a Partial Differential Equations. $3 890899
650 2 4 $a Mathematical Methods in Physics. $3 890898
650 2 4 $a Mathematical Applications in the Physical Sciences. $3 1566152
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer eBooks
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-17954-4
950 $a Mathematics and Statistics (Springer-11649)