Liouville’s Theory in Linear and Nonlinear Partial Differential Equations

Takashi Suzuki (Autor)

Buch | Hardcover

589 Seiten

2025
Springer Verlag, Singapore
978-981-95-1974-3 (ISBN)

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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.

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

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

Erscheinungsdatum	05.11.2025
Reihe/Serie	Springer Asia Pacific Mathematics Series
Zusatzinfo	1 Illustrations, black and white
Verlagsort	Singapore
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	Inverse Strum-Liouville problem • nonlinear elliptic equation • Non-standard elliptic regularity • Self-Organization • transport theory
ISBN-10	981-95-1974-8 / 9819519748
ISBN-13	978-981-95-1974-3 / 9789819519743
Zustand	Neuware