國立高雄大學圖資館 |

Pseudo-monotone operator theory for unsteady problems with variable exponents

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Pseudo-monotone operator theory for unsteady problems with variable exponentsby Alex Kaltenbach.
作者:	Kaltenbach, Alex.
出版者:	Cham :Springer International Publishing :2023.
面頁冊數:	xiii, 358 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Monotone operators.
電子資源:	https://doi.org/10.1007/978-3-031-29670-3
ISBN:	9783031296703$q(electronic bk.)

Pseudo-monotone operator theory for unsteady problems with variable exponents
Kaltenbach, Alex.

Pseudo-monotone operator theory for unsteady problems with variable exponents[electronic resource] /by Alex Kaltenbach. - Cham :Springer International Publishing :2023. - xiii, 358 p. :ill., digital ;24 cm. - Lecture notes in mathematics,v. 23291617-9692 ;. - Lecture notes in mathematics ;2035..

This book provides a comprehensive analysis of the existence of weak solutions of unsteady problems with variable exponents. The central motivation is the weak solvability of the unsteady p(.,.)-Navier-Stokes equations describing the motion of an incompressible electro-rheological fluid. Due to the variable dependence of the power-law index p(.,.) in this system, the classical weak existence analysis based on the pseudo-monotone operator theory in the framework of Bochner-Lebesgue spaces is not applicable. As a substitute for Bochner-Lebesgue spaces, variable Bochner-Lebesgue spaces are introduced and analyzed. In the mathematical framework of this substitute, the theory of pseudo-monotone operators is extended to unsteady problems with variable exponents, leading to the weak solvability of the unsteady p(.,.)-Navier-Stokes equations under general assumptions. Aimed primarily at graduate readers, the book develops the material step-by-step, starting with the basics of PDE theory and non-linear functional analysis. The concise introductions at the beginning of each chapter, together with illustrative examples, graphics, detailed derivations of all results and a short summary of the functional analytic prerequisites, will ease newcomers into the subject.

ISBN: 9783031296703$q(electronic bk.)

Standard No.: 10.1007/978-3-031-29670-3doiSubjects--Topical Terms:

274794
Monotone operators.

LC Class. No.: QA329.8 / .K35 2023

Dewey Class. No.: 515.724

Pseudo-monotone operator theory for unsteady problems with variable exponents
LDR:02333nmm a2200325 a 4500 001 647887
003 DE-He213
005 20230811200235.0
006 m d
007 cr nn 008maaau
008 240116s2023 sz s 0 eng d
020 $a 9783031296703$q(electronic bk.)
020 $a 9783031296697$q(paper)
024 7 $a 10.1007/978-3-031-29670-3 $2 doi
035 $a 978-3-031-29670-3
040 $a GP $c GP
041 0 $a eng
050 4 $a QA329.8 $b .K35 2023
072 7 $a PBKF $2 bicssc
072 7 $a MAT037000 $2 bisacsh
072 7 $a PBKF $2 thema
082 0 4 $a 515.724 $2 23
090 $a QA329.8 $b .K14 2023
100 1 $a Kaltenbach, Alex. $3 957395
245 1 0 $a Pseudo-monotone operator theory for unsteady problems with variable exponents $h [electronic resource] / $c by Alex Kaltenbach.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2023.
300 $a xiii, 358 p. : $b ill., digital ; $c 24 cm.
490 1 $a Lecture notes in mathematics, $x 1617-9692 ; $v v. 2329
520 $a This book provides a comprehensive analysis of the existence of weak solutions of unsteady problems with variable exponents. The central motivation is the weak solvability of the unsteady p(.,.)-Navier-Stokes equations describing the motion of an incompressible electro-rheological fluid. Due to the variable dependence of the power-law index p(.,.) in this system, the classical weak existence analysis based on the pseudo-monotone operator theory in the framework of Bochner-Lebesgue spaces is not applicable. As a substitute for Bochner-Lebesgue spaces, variable Bochner-Lebesgue spaces are introduced and analyzed. In the mathematical framework of this substitute, the theory of pseudo-monotone operators is extended to unsteady problems with variable exponents, leading to the weak solvability of the unsteady p(.,.)-Navier-Stokes equations under general assumptions. Aimed primarily at graduate readers, the book develops the material step-by-step, starting with the basics of PDE theory and non-linear functional analysis. The concise introductions at the beginning of each chapter, together with illustrative examples, graphics, detailed derivations of all results and a short summary of the functional analytic prerequisites, will ease newcomers into the subject.
650 0 $a Monotone operators. $3 274794
650 0 $a Navier-Stokes equations. $3 229271
650 1 4 $a Functional Analysis. $3 274845
650 2 4 $a Engineering Fluid Dynamics. $3 273893
650 2 4 $a Operator Theory. $3 274795
650 2 4 $a Differential Equations. $3 285983
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a Lecture notes in mathematics ; $v 2035. $3 557764
856 4 0 $u https://doi.org/10.1007/978-3-031-29670-3
950 $a Mathematics and Statistics (SpringerNature-11649)