An Asymptotic Analysis for a Nonstandard Cahn-Hilliard System with Viscosity - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Asymptotic Analysis for a Nonstandard Cahn-Hilliard System with Viscosity write by . This book was released on 2011. An Asymptotic Analysis for a Nonstandard Cahn-Hilliard System with Viscosity available in PDF, EPUB and Kindle.
Limiting Problems for a Nonstandard Viscous Cahn-Hilliard System with Dynamic Boundary Conditions
Limiting Problems for a Nonstandard Viscous Cahn-Hilliard System with Dynamic Boundary Conditions - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Limiting Problems for a Nonstandard Viscous Cahn-Hilliard System with Dynamic Boundary Conditions write by Pierluigi Colli. This book was released on 2017. Limiting Problems for a Nonstandard Viscous Cahn-Hilliard System with Dynamic Boundary Conditions available in PDF, EPUB and Kindle. This note is concerned with a nonlinear diffusion problem of phase-field type, consisting of a parabolic system of two partial differential equations, complemented by boundary and initial conditions. The system arises from a model of two-species phase segregation on an atomic lattice and was introduced by Podio-Guidugli in Ric. Mat. 55 (2006), pp. 105-118. The two unknowns are the phase parameter and the chemical potential. In contrast to previous investigations about this PDE system, we consider here a dynamic boundary condition for the phase variable that involves the Laplace-Beltrami operator and models an additional nonconserving phase transition occurring on the surface of the domain. We are interested to some asymptotic analysis and first discuss the asymptotic limit of the system as the viscosity coefficient of the order parameter equation tends to 0: the convergence of solutions to the corresponding solutions for the limit problem is proven. Then, we study the long-time behavior of the system for both problems, with positive or zero viscosity coefficient, and characterize the omega-limit set in both cases.
Solvability, Regularity, and Optimal Control of Boundary Value Problems for PDEs
Solvability, Regularity, and Optimal Control of Boundary Value Problems for PDEs - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Solvability, Regularity, and Optimal Control of Boundary Value Problems for PDEs write by Pierluigi Colli. This book was released on 2017-11-03. Solvability, Regularity, and Optimal Control of Boundary Value Problems for PDEs available in PDF, EPUB and Kindle. This volume gathers contributions in the field of partial differential equations, with a focus on mathematical models in phase transitions, complex fluids and thermomechanics. These contributions are dedicated to Professor Gianni Gilardi on the occasion of his 70th birthday. It particularly develops the following thematic areas: nonlinear dynamic and stationary equations; well-posedness of initial and boundary value problems for systems of PDEs; regularity properties for the solutions; optimal control problems and optimality conditions; feedback stabilization and stability results. Most of the articles are presented in a self-contained manner, and describe new achievements and/or the state of the art in their line of research, providing interested readers with an overview of recent advances and future research directions in PDEs.
Topics in Applied Analysis and Optimisation
Topics in Applied Analysis and Optimisation - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Topics in Applied Analysis and Optimisation write by Michael Hintermüller. This book was released on 2019-11-27. Topics in Applied Analysis and Optimisation available in PDF, EPUB and Kindle. This volume comprises selected, revised papers from the Joint CIM-WIAS Workshop, TAAO 2017, held in Lisbon, Portugal, in December 2017. The workshop brought together experts from research groups at the Weierstrass Institute in Berlin and mathematics centres in Portugal to present and discuss current scientific topics and to promote existing and future collaborations. The papers include the following topics: PDEs with applications to material sciences, thermodynamics and laser dynamics, scientific computing, nonlinear optimization and stochastic analysis.
The Cahn–Hilliard Equation: Recent Advances and Applications
The Cahn–Hilliard Equation: Recent Advances and Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Cahn–Hilliard Equation: Recent Advances and Applications write by Alain Miranville. This book was released on 2019-09-09. The Cahn–Hilliard Equation: Recent Advances and Applications available in PDF, EPUB and Kindle. 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.
