Alain Damlamian's Books

Multiscale Problems

Theory, Numerical Approximation and Applications

By: Alain Damlamian,Bernadette Miara,Daqian Li

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Multiscale Problems

Theory, Numerical Approximation and Applications

By: Alain Damlamian,Bernadette Miara,Daqian Li

The focus of this is on the latest developments related to the analysis of problems in which several scales are presented. After a theoretical presentation of the theory of homogenization in the periodic case, the other contributions address a wide range of applications in the fields of elasticity (asymptotic behavior of nonlinear elastic thin structures, modeling of junction of a periodic family of rods with a plate) and fluid mechanics (stationary Navier?Stokes equations in porous media). Other applications concern the modeling of new composites (electromagnetic and piezoelectric materials) and imperfect transmission problems. A detailed approach of numerical finite element methods is also investigated.

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Page Count

314

Publisher

World Scientific

Published Date

ISBN 10

9814366889

ISBN 13

9789814366885

The Periodic Unfolding Method

Theory and Applications to Partial Differential Problems

By: Doina Cioranescu,Alain Damlamian,Georges Griso

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The Periodic Unfolding Method

Theory and Applications to Partial Differential Problems

By: Doina Cioranescu,Alain Damlamian,Georges Griso

This is the first book on the subject of the periodic unfolding method (originally called "éclatement périodique" in French), which was originally developed to clarify and simplify many questions arising in the homogenization of PDE's. It has since led to the solution of some open problems. Written by the three mathematicians who developed the method, the book presents both the theory as well as numerous examples of applications for partial differential problems with rapidly oscillating coefficients: in fixed domains (Part I), in periodically perforated domains (Part II), and in domains with small holes generating a strange term (Part IV). The method applies to the case of multiple microscopic scales (with finitely many distinct scales) which is connected to partial unfolding (also useful for evolution problems). This is discussed in the framework of oscillating boundaries (Part III). A detailed example of its application to linear elasticity is presented in the case of thin elastic plates (Part V). Lastly, a complete determination of correctors for the model problem in Part I is obtained (Part VI). This book can be used as a graduate textbook to introduce the theory of homogenization of partial differential problems, and is also a must for researchers interested in this field.

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Page Count

508

Publisher

Springer

Published Date

ISBN 10

9811330328

ISBN 13

9789811330322

Semi-Linear Hyperbolic Problems in Bounded Domains

By: Alain Haraux

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Semi-Linear Hyperbolic Problems in Bounded Domains

By: Alain Haraux

The opening chapter provides background information on the basic functional setting, semi-groups and the abstract wave equation, almost periodicity and the wave equation, and technical tools. Succeeding chapters cover the initial value problem, asymptotics in autonomous cases, non-resonance in the purely dissipative case, stability of periodic and almost-periodic solutions, oscillation properties in the conservative case, and global properties of the full equation. Includes bibliographic references and indexes by author and subject.

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Page Count

316

Publisher

CRC Press

Published Date

ISBN 10

3718604604

ISBN 13

9783718604609

Mathematical Methods and Models in Phase Transitions

By: Alain Miranville

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Mathematical Methods and Models in Phase Transitions

By: Alain Miranville

The modelling and the study of phase transition phenomena are capital issues as they have essential applications in material sciences and in biological and industrial processes. We can mention, e.g., phase separation in alloys, ageing of materials, microstructure evolution, crystal growth, solidification in complex alloys, surface diffusion in the presence of stress, evolution of the surface of a thin flow in heteroepitaxial growth, motion of voids in interconnects in integrated circuits, treatment of airway closure disease by surfactant injection, fuel injection, fire extinguishers etc., This book consists of 11 contributions from specialists in the mathematical modelling and analysis of phase transitions. The content of these contributions ranges from the modelling to the mathematical and numerical analysis. Furthermore, many numerical simulations are presented. Finally, the contributors have tried to give comprehensive and accurate reference lists. This book should thus serve as a reference book for researchers interested in phase transition phenomena.

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Page Count

306

Publisher

Nova Publishers

Published Date

ISBN 10

1594543178

ISBN 13

9781594543173

Multiscale Problems

Theory, Numerical Approximation and Applications

By: Alain Damlamian

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Multiscale Problems

Theory, Numerical Approximation and Applications

By: Alain Damlamian

The focus of this is on the latest developments related to the analysis of problems in which several scales are presented. After a theoretical presentation of the theory of homogenization in the periodic case, the other contributions address a wide range of applications in the fields of elasticity (asymptotic behavior of nonlinear elastic thin structures, modeling of junction of a periodic family of rods with a plate) and fluid mechanics (stationary NavierOCoStokes equations in porous media). Other applications concern the modeling of new composites (electromagnetic and piezoelectric materials) and imperfect transmission problems. A detailed approach of numerical finite element methods is also investigated.

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Page Count

314

Publisher

World Scientific

Published Date

ISBN 10

9814366897

ISBN 13

9789814366892

The Periodic Unfolding Method

Theory and Applications to Partial Differential Problems

By: Doina Cioranescu,Alain Damlamian,Georges Griso

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The Periodic Unfolding Method

Theory and Applications to Partial Differential Problems

By: Doina Cioranescu,Alain Damlamian,Georges Griso

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N/A

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Solve jigsaw puzzle

Age

Page Count

508

Publisher

Springer

Published Date

ISBN 10

9811330328

ISBN 13

9789811330322

Book's by Alain Damlamian

Multiscale Problems

Multiscale Problems

The Periodic Unfolding Method

The Periodic Unfolding Method

Semi-Linear Hyperbolic Problems in Bounded Domains

Semi-Linear Hyperbolic Problems in Bounded Domains

Mathematical Methods and Models in Phase Transitions

Mathematical Methods and Models in Phase Transitions

Multiscale Problems

Multiscale Problems

The Periodic Unfolding Method

The Periodic Unfolding Method

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