Methods Of Geometry In The Theory Of Partial Differential Equations: Principle Of The Cancellation Of Singularities
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A01=Takashi Suzuki
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Analytic Mechanics
Author_Takashi Suzuki
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Biological Model
Blowup of the Solution
Blowup Rate
Boltzmann Poisson Equation
Category1=Non-Fiction
Category=PBKJ
Category=PBMP
Center Manifold
Chemotaxis
Concentration Compactness
COP=Singapore
Curvatures
Curves and Surfaces
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Differential Forms
Elliptic Regularity
eq_isMigrated=0
eq_isMigrated=2
eq_nobargain
Filtration
Free Boundary Problem
Free Energy
Global Analysis
Hadamard's Variational Formula
Hamilton Mechanics
Interface Vanishing
Language_English
Liouville Integral
Liouville's Formula
Logarithmic Diffusion
Lotka Volterra Systems
Magnet-Encephalography
Maxwell Equation
Minkowski Space
Moser's Iteration Scheme
Nonlinear Partial Differential Equations
Onsager's Theory
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Perturbation of Eigenvalues
Point Vortices
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Quantized Blowup Mechanism
Ricci Flow
Riemann Geometry
Sectional Curvatures
Semilinear Elliptic Equations
Smoluchowski Poisson Equation
softlaunch
Statistical Mechanics
Stefan Condition
Symplectic Manifolds
Theory of Dynamical Systems
Theory of Gradient Inequality
Theory of Harmonic Integration
Theory of Integrable Systems
TrudingerAcAEURA"Moser Inequality
Product details
- ISBN 9789811287893
- Publication Date: 16 Feb 2024
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
- Language: English
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Mathematical models are used to describe the essence of the real world, and their analysis induces new predictions filled with unexpected phenomena.In spite of a huge number of insights derived from a variety of scientific fields in these five hundred years of the theory of differential equations, and its extensive developments in these one hundred years, several principles that ensure these successes are discovered very recently.This monograph focuses on one of them: cancellation of singularities derived from interactions of multiple species, which is described by the language of geometry, in particular, that of global analysis.Five objects of inquiry, scattered across different disciplines, are selected in this monograph: evolution of geometric quantities, models of multi-species in biology, interface vanishing of d - δ systems, the fundamental equation of electro-magnetic theory, and free boundaries arising in engineering.The relaxation of internal tensions in these systems, however, is described commonly by differential forms, and the reader will be convinced of further applications of this principle to other areas.
