Liouville's Theory in Linear and Nonlinear Partial Differential Equations

Erscheinungsjahr 2025
ISBN: 978-981-951974-3
Verlag: Springer

Buch, Englisch, 589 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1066 g

Reihe: 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.

Zielgruppe

Research

Autoren/Hrsg.

Suzuki, Takashi

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie

Inhaltsverzeichnis

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

Über Autor(innen)

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