Liouville’s Theory in Linear and Nonlinear Partial Differential Equations

Takashi Suzuki

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English

Springer Verlag, Singapore
05 December 2025

Functional analysis & transforms; Differential calculus & equations; Differential & Riemannian geometry

Series: Springer Asia Pacific Mathematics Series

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.

By: Takashi Suzuki
Imprint: Springer Verlag, Singapore
Country of Publication: Singapore
Dimensions: Height: 235mm, Width: 155mm,
ISBN: 9789819519743
ISBN 10: 9819519748
Series: Springer Asia Pacific Mathematics Series
Pages: 589
Publication Date: 05 December 2025
Audience: Professional and scholarly , College/higher education , Undergraduate , Further / Higher Education
Format: Hardback
Publisher's Status: Forthcoming

Takashi Suzuki is a Vice-Director of the Center for Mathematical Modeling and Data Science at Osaka Univeristy.