Abstract Parabolic Evolution Equations and their Applications

• Main Author: Yagi, Atsushi (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2010.
• Series: Springer Monographs in Mathematics,
• Subjects: Mathematics.; Dynamics.; Ergodic theory.; Partial differential equations.; Biomathematics.; Partial Differential Equations.; Dynamical Systems and Ergodic Theory.; Mathematical and Computational Biology.

The semigroup methods are known as a powerful tool for analyzing nonlinear diffusion equations and systems. The author has studied abstract parabolic evolution equations and their applications to nonlinear diffusion equations and systems for more than 30 years. He gives first, after reviewing the th...

Table of Contents:

• Preliminaries
• Sectorial Operators
• Linear Evolution Equations
• Semilinear Evolution Equations
• Quasilinear Evolution Equations
• Dynamical Systems
• Numerical Analysis
• Semiconductor Models
• Activator–Inhibitor Models
• Belousov–Zhabotinskii Reaction Models
• Forest Kinematic Model
• Chemotaxis Models
• Termite Mound Building Model
• Adsorbate-Induced Phase Transition Model
• Lotka–Volterra Competition Model with Cross-Diffusion
• Characterization of Domains of Fractional Powers.