Liouville’s Theory in Linear and Nonlinear Partial Differential Equations / by Takashi Suzuki.

Format:

Book

Author/Creator:

Suzuki, Takashi.

Series:

Springer Asia Pacific Mathematics Series, 3091-2563 ; 8

Language:

English

Subjects (All):

Mathematical analysis.

Functional analysis.

Geometry, Differential.

Analysis.

Functional Analysis.

Differential Geometry.

Local Subjects:

Analysis.

Functional Analysis.

Differential Geometry.

Physical Description:

1 online resource (853 pages)

Edition:

1st ed. 2025.

Place of Publication:

Singapore : Springer Nature Singapore : Imprint: Springer, 2025.

Summary:

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.

Contents:

1 Spectral Theory

2 Surface Theory

3 Elliptic Theory: A Classical and Modern Study

4 Transformation Theory

5 Potentials of Self-Organization: A Fusion.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

9789819519750

OCLC:

1548323221