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Liouville's theory in linear and nonlinear partial differential equations

Record Type:	Electronic resources : Monograph/item
Title/Author:	Liouville's theory in linear and nonlinear partial differential equations/ by Takashi Suzuki.
Author:	Suzuki, Takashi.
Published:	Singapore :Springer Nature Singapore : : 2025.,
Description:	xv, 589 p. :ill., digital ;24 cm.
[NT 15003449]:	1 Spectral Theory -- 2 Surface Theory -- 3 Elliptic Theory: A Classical and Modern Study -- 4 Transformation Theory -- 5 Potentials of Self-Organization: A Fusion.
Contained By:	Springer Nature eBook
Subject:	Differential equations, Partial. -
Online resource:	https://doi.org/10.1007/978-981-95-1975-0
ISBN:	9789819519750

Liouville's theory in linear and nonlinear partial differential equations
Suzuki, Takashi.

Liouville's theory in linear and nonlinear partial differential equations[electronic resource] /by Takashi Suzuki. - Singapore :Springer Nature Singapore :2025. - xv, 589 p. :ill., digital ;24 cm. - Springer Asia pacific mathematics series,v. 83091-2563 ;. - Springer Asia pacific mathematics series ;v. 8..

1 Spectral Theory -- 2 Surface Theory -- 3 Elliptic Theory: A Classical and Modern Study -- 4 Transformation Theory -- 5 Potentials of Self-Organization: A Fusion.

A variety of theorems named the Liouville property play fundamental roles in modern theory of mathematical analysis. Understanding each of them individually is not so difficult nowadays. What are they pointing toward in their totality, however? This monograph asserts that self-organization may be an answer, searching recent studies on linear and nonlinear partial differential equations. Critical breakthroughs have emerged in accordance with the widely spread classical ideas of J. Liouville in various forms, that is, the spectral, elliptic, surface, and transport theories, in turn. A fusion of them is seen in recently developing research fields-mathematical oncology, non-equilibrium statistical mechanics, dynamical theory, and shape optimization-which taken together may be called the potential for self-organization.

ISBN: 9789819519750

Standard No.: 10.1007/978-981-95-1975-0doiSubjects--Topical Terms:

518115
Differential equations, Partial.

LC Class. No.: QA377

Dewey Class. No.: 515.353

Liouville's theory in linear and nonlinear partial differential equations
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490 1 $a Springer Asia pacific mathematics series, $x 3091-2563 ; $v v. 8
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520 $a A variety of theorems named the Liouville property play fundamental roles in modern theory of mathematical analysis. Understanding each of them individually is not so difficult nowadays. What are they pointing toward in their totality, however? This monograph asserts that self-organization may be an answer, searching recent studies on linear and nonlinear partial differential equations. Critical breakthroughs have emerged in accordance with the widely spread classical ideas of J. Liouville in various forms, that is, the spectral, elliptic, surface, and transport theories, in turn. A fusion of them is seen in recently developing research fields-mathematical oncology, non-equilibrium statistical mechanics, dynamical theory, and shape optimization-which taken together may be called the potential for self-organization.
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650 0 $a Sturm-Liouville equation. $3 705282
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