Language:
English
繁體中文
Help
Login
Back
Switch To:
Labeled
|
MARC Mode
|
ISBD
Theory and Applications of Abstract ...
~
Ruan, Shigui.
Theory and Applications of Abstract Semilinear Cauchy Problems
Record Type:
Language materials, printed : Monograph/item
Title/Author:
Theory and Applications of Abstract Semilinear Cauchy Problems/ by Pierre Magal, Shigui Ruan.
Author:
Magal, Pierre.
other author:
Ruan, Shigui.
Description:
XXII, 543 p. 17 illus., 10 illus. in color.online resource. :
Contained By:
Springer Nature eBook
Subject:
Differential equations. -
Online resource:
https://doi.org/10.1007/978-3-030-01506-0
ISBN:
9783030015060
Theory and Applications of Abstract Semilinear Cauchy Problems
Magal, Pierre.
Theory and Applications of Abstract Semilinear Cauchy Problems
[electronic resource] /by Pierre Magal, Shigui Ruan. - 1st ed. 2018. - XXII, 543 p. 17 illus., 10 illus. in color.online resource. - Applied Mathematical Sciences,2010066-5452 ;. - Applied Mathematical Sciences,191.
Chapter 1- Introduction -- Chapter 2- Semigroups and Hille-Yosida Theorem -- Chapter 3- Integrated Semigroups and Cauchy Problems with Non-dense Domain -- Chapter 4- Spectral Theory for Linear Operators -- Chapter 5- Semilinear Cauchy Problems with Non-dense Domain -- Chapter 6- Center Manifolds, Hopf Bifurcation and Normal Forms -- Chapter 7- Functional Differential Equations -- Chapter 8- Age-structured Models -- Chapter 9- Parabolic Equations -- References -- Index.
Several types of differential equations, such as functional differential equation, age-structured models, transport equations, reaction-diffusion equations, and partial differential equations with delay, can be formulated as abstract Cauchy problems with non-dense domain. This monograph provides a self-contained and comprehensive presentation of the fundamental theory of non-densely defined semilinear Cauchy problems and their applications. Starting from the classical Hille-Yosida theorem, semigroup method, and spectral theory, this monograph introduces the abstract Cauchy problems with non-dense domain, integrated semigroups, the existence of integrated solutions, positivity of solutions, Lipschitz perturbation, differentiability of solutions with respect to the state variable, and time differentiability of solutions. Combining the functional analysis method and bifurcation approach in dynamical systems, then the nonlinear dynamics such as the stability of equilibria, center manifold theory, Hopf bifurcation, and normal form theory are established for abstract Cauchy problems with non-dense domain. Finally applications to functional differential equations, age-structured models, and parabolic equations are presented. This monograph will be very valuable for graduate students and researchers in the fields of abstract Cauchy problems, infinite dimensional dynamical systems, and their applications in biological, chemical, medical, and physical problems.
ISBN: 9783030015060
Standard No.: 10.1007/978-3-030-01506-0doiSubjects--Topical Terms:
527664
Differential equations.
LC Class. No.: QA372
Dewey Class. No.: 515.352
Theory and Applications of Abstract Semilinear Cauchy Problems
LDR
:03347nam a22003975i 4500
001
988319
003
DE-He213
005
20200705125921.0
007
cr nn 008mamaa
008
201225s2018 gw | s |||| 0|eng d
020
$a
9783030015060
$9
978-3-030-01506-0
024
7
$a
10.1007/978-3-030-01506-0
$2
doi
035
$a
978-3-030-01506-0
050
4
$a
QA372
072
7
$a
PBKJ
$2
bicssc
072
7
$a
MAT007000
$2
bisacsh
072
7
$a
PBKJ
$2
thema
082
0 4
$a
515.352
$2
23
100
1
$a
Magal, Pierre.
$4
aut
$4
http://id.loc.gov/vocabulary/relators/aut
$3
680107
245
1 0
$a
Theory and Applications of Abstract Semilinear Cauchy Problems
$h
[electronic resource] /
$c
by Pierre Magal, Shigui Ruan.
250
$a
1st ed. 2018.
264
1
$a
Cham :
$b
Springer International Publishing :
$b
Imprint: Springer,
$c
2018.
300
$a
XXII, 543 p. 17 illus., 10 illus. in color.
$b
online resource.
336
$a
text
$b
txt
$2
rdacontent
337
$a
computer
$b
c
$2
rdamedia
338
$a
online resource
$b
cr
$2
rdacarrier
347
$a
text file
$b
PDF
$2
rda
490
1
$a
Applied Mathematical Sciences,
$x
0066-5452 ;
$v
201
505
0
$a
Chapter 1- Introduction -- Chapter 2- Semigroups and Hille-Yosida Theorem -- Chapter 3- Integrated Semigroups and Cauchy Problems with Non-dense Domain -- Chapter 4- Spectral Theory for Linear Operators -- Chapter 5- Semilinear Cauchy Problems with Non-dense Domain -- Chapter 6- Center Manifolds, Hopf Bifurcation and Normal Forms -- Chapter 7- Functional Differential Equations -- Chapter 8- Age-structured Models -- Chapter 9- Parabolic Equations -- References -- Index.
520
$a
Several types of differential equations, such as functional differential equation, age-structured models, transport equations, reaction-diffusion equations, and partial differential equations with delay, can be formulated as abstract Cauchy problems with non-dense domain. This monograph provides a self-contained and comprehensive presentation of the fundamental theory of non-densely defined semilinear Cauchy problems and their applications. Starting from the classical Hille-Yosida theorem, semigroup method, and spectral theory, this monograph introduces the abstract Cauchy problems with non-dense domain, integrated semigroups, the existence of integrated solutions, positivity of solutions, Lipschitz perturbation, differentiability of solutions with respect to the state variable, and time differentiability of solutions. Combining the functional analysis method and bifurcation approach in dynamical systems, then the nonlinear dynamics such as the stability of equilibria, center manifold theory, Hopf bifurcation, and normal form theory are established for abstract Cauchy problems with non-dense domain. Finally applications to functional differential equations, age-structured models, and parabolic equations are presented. This monograph will be very valuable for graduate students and researchers in the fields of abstract Cauchy problems, infinite dimensional dynamical systems, and their applications in biological, chemical, medical, and physical problems.
650
0
$a
Differential equations.
$3
527664
650
0
$a
Partial differential equations.
$3
1102982
650
1 4
$a
Ordinary Differential Equations.
$3
670854
650
2 4
$a
Partial Differential Equations.
$3
671119
700
1
$a
Ruan, Shigui.
$4
aut
$4
http://id.loc.gov/vocabulary/relators/aut
$3
680108
710
2
$a
SpringerLink (Online service)
$3
593884
773
0
$t
Springer Nature eBook
776
0 8
$i
Printed edition:
$z
9783030015053
776
0 8
$i
Printed edition:
$z
9783030015077
830
0
$a
Applied Mathematical Sciences,
$x
0066-5452 ;
$v
191
$3
1254006
856
4 0
$u
https://doi.org/10.1007/978-3-030-01506-0
912
$a
ZDB-2-SMA
912
$a
ZDB-2-SXMS
950
$a
Mathematics and Statistics (SpringerNature-11649)
950
$a
Mathematics and Statistics (R0) (SpringerNature-43713)
based on 0 review(s)
Multimedia
Reviews
Add a review
and share your thoughts with other readers
Export
pickup library
Processing
...
Change password
Login