Overview

This is the first book to present a detailed discussion of both classical and recent results on the popular Cahn–Hilliard equation and some of its variants. The focus is on mathematical analysis of Cahn–Hilliard models, with an emphasis on thermodynamically relevant logarithmic nonlinear terms, for which several questions are still open. Initially proposed in view of applications to materials science, the Cahn–Hilliard equation is now applied in many other areas, including image processing, biology, ecology, astronomy, and chemistry. In particular, the author addresses applications to image inpainting and tumor growth. Many chapters include open problems and directions for future research. The Cahn?Hilliard Equation: Recent Advances and Applications is intended for graduate students and researchers in applied mathematics, especially those interested in phase separation models and their generalizations and applications to other fields. Materials scientists also will find this text of interest.

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9781611975918

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Alain Miranville is Distinguished Professor of applied mathematics at the University of Poitiers, France. He is also Invited Chair Professor at Xiamen University, Distinguished Adjunct Professor at Henan Normal University, and 2018 Fudan Fellow at Fudan University, all three in China. His research interests include the qualitative study of parabolic partial differential equations, the investigation of infinite-dimensional dynamical systems, and the study of models in phase separation and transition, image processing, and medicine.

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