On the Unique Solvability of a Nonlocal Phase Separation Problem for Multicomponent Systems PDF Download
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Author: Jens André Griepentrog
Publisher:
ISBN:
Category :
Languages : en
Pages : 13
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Author: Jens André Griepentrog
Publisher:
ISBN:
Category :
Languages : en
Pages : 13
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Author: Piotr Biler
Publisher:
ISBN:
Category : Differential equations, Elliiptics
Languages : en
Pages : 362
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Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 958
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Author:
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ISBN:
Category : Differential equations
Languages : en
Pages : 378
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Author: Pierluigi Colli
Publisher:
ISBN:
Category :
Languages : en
Pages :
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This paper investigates a nonlocal version of a model for phase separation on an atomic lattice that was introduced by P. Podio-Guidugli in Ric. Mat. 55 (2006) 105-118. The model consists of an initial-boundary value problem for a nonlinearly coupled system of two partial differential equations governing the evolution of an order parameter p and the chemical potential my. Singular contributions to the local free energy in the form of logarithmic or ouble-obstacle potentials are admitted. In contrast to the local model, which was studied by P. Podio-Guidugli and the present authors in a series of recent publications, in the nonlocal case the equation governing the evolution of the order parameter contains in place of the Laplacian a nonlocal expression that originates from nonlocal contributions to the free energy and accounts for possible long-range interactions between the atoms. It is shown that just as in the local case the model equations are well posed, where the technique of proving existence is entirely different: it is based on an application of Tikhonov's fixed point theorem in a rather unusual separable and reflexive Banach space.
Author: Michael Hintermüller
Publisher: Springer Nature
ISBN: 3030331164
Category : Mathematics
Languages : en
Pages : 396
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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.
Author: Alain Miranville
Publisher: SIAM
ISBN: 1611975921
Category : Mathematics
Languages : en
Pages : 216
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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.
Author: Andrei D. Polyanin
Publisher: CRC Press
ISBN: 1135440816
Category : Mathematics
Languages : en
Pages : 835
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The Handbook of Nonlinear Partial Differential Equations is the latest in a series of acclaimed handbooks by these authors and presents exact solutions of more than 1600 nonlinear equations encountered in science and engineering--many more than any other book available. The equations include those of parabolic, hyperbolic, elliptic and other types, and the authors pay special attention to equations of general form that involve arbitrary functions. A supplement at the end of the book discusses the classical and new methods for constructing exact solutions to nonlinear equations. To accommodate different mathematical backgrounds, the authors avoid wherever possible the use of special terminology, outline some of the methods in a schematic, simplified manner, and arrange the equations in increasing order of complexity. Highlights of the Handbook:
Author: Joachim Escher
Publisher: Birkhäuser
ISBN: 9783034800747
Category : Mathematics
Languages : en
Pages : 717
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The volume originates from the 'Conference on Nonlinear Parabolic Problems' held in celebration of Herbert Amann's 70th birthday at the Banach Center in Bedlewo, Poland. It features a collection of peer-reviewed research papers by recognized experts highlighting recent advances in fields of Herbert Amann's interest such as nonlinear evolution equations, fluid dynamics, quasi-linear parabolic equations and systems, functional analysis, and more.
Author:
Publisher:
ISBN:
Category : Mechanics, Applied
Languages : en
Pages : 620
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