Regularity Results for Nonlinear Elliptic Systems and Applications
Regularity Results for Nonlinear Elliptic Systems and Applications

Author: Alain Bensoussan

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 450

ISBN-13: 3662129051

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This book collects many helpful techniques for obtaining regularity results for solutions of nonlinear systems of partial differential equations. These are applied in various cases to provide useful examples and relevant results, particularly in such fields as fluid mechanics, solid mechanics, semiconductor theory and game theory.

Boundary Value Problems, Integral Equations and Related Problems
Boundary Value Problems, Integral Equations and Related Problems

Author: Guo Chun Wen

Publisher: World Scientific

Published: 2011

Total Pages: 436

ISBN-13: 9814327867

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In this volume, we report new results about various boundary value problems for partial differential equations and functional equations, theory and methods of integral equations and integral operators including singular integral equations, applications of boundary value problems and integral equations to mechanics and physics, numerical methods of integral equations and boundary value problems, theory and methods for inverse problems of mathematical physics, Clifford analysis and related problems. Contributors include: L Baratchart, B L Chen, D C Chen, S S Ding, K Q Lan, A Farajzadeh, M G Fei, T Kosztolowicz, A Makin, T Qian, J M Rassias, J Ryan, C-Q Ru, P Schiavone, P Wang, Q S Zhang, X Y Zhang, S Y Du, H Y Gao, X Li, Y Y Qiao, G C Wen, Z T Zhang, and others.

IUTAM Symposium on Theoretical, Computational and Modelling Aspects of Inelastic Media
IUTAM Symposium on Theoretical, Computational and Modelling Aspects of Inelastic Media

Author: B. Daya Reddy

Publisher: Springer Science & Business Media

Published: 2008-09-24

Total Pages: 388

ISBN-13: 1402090900

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This work comprises papers based on some of the talks presented at the IUTAM Symposium of the same name, held in Cape Town, January 14-18, 2008. This volume treats cutting-edge issues in modelling, the behaviour of various classes of inelastic media, and associated algorithms for carrying out computational simulations. A key feature of the contributions are works directed at modelling behaviour at the meso and micro-scales, and at bridging the micro-macro scales.

Cross Diffusion Systems
Cross Diffusion Systems

Author: Dung Le

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2022-10-24

Total Pages: 236

ISBN-13: 3110795132

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The introduction of cross diffusivity opens many questions in the theory of reactiondiffusion systems. This book will be the first to investigate such problems presenting new findings for researchers interested in studying parabolic and elliptic systems where classical methods are not applicable. In addition, The Gagliardo-Nirenberg inequality involving BMO norms is improved and new techniques are covered that will be of interest. This book also provides many open problems suitable for interested Ph.D students.

Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105), Volume 105
Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105), Volume 105

Author: Mariano Giaquinta

Publisher: Princeton University Press

Published: 2016-03-02

Total Pages: 309

ISBN-13: 1400881625

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A classic treatment of multiple integrals in the calculus of variations and nonlinear elliptic systems from the acclaimed Annals of Mathematics Studies series Princeton University Press is proud to have published the Annals of Mathematics Studies since 1940. One of the oldest and most respected series in science publishing, it has included many of the most important and influential mathematical works of the twentieth century. The series continues this tradition as Princeton University Press publishes the major works of the twenty-first century. To mark the continued success of the series, all books are available in paperback and as ebooks.

The Energy Method, Stability, and Nonlinear Convection
The Energy Method, Stability, and Nonlinear Convection

Author: brian straughan

Publisher: Springer Science & Business Media

Published: 2003-10-01

Total Pages: 470

ISBN-13: 9780387004532

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Six new chapters (14-19) deal with topics of current interest: multi-component convection diffusion, convection in a compressible fluid, convenction with temperature dependent viscosity and thermal conductivity, penetrative convection, nonlinear stability in ocean circulation models, and numerical solution of eigenvalue problems.

Mean Field Games and Mean Field Type Control Theory
Mean Field Games and Mean Field Type Control Theory

Author: Alain Bensoussan

Publisher: Springer Science & Business Media

Published: 2013-10-16

Total Pages: 132

ISBN-13: 1461485088

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​Mean field games and Mean field type control introduce new problems in Control Theory. The terminology “games” may be confusing. In fact they are control problems, in the sense that one is interested in a single decision maker, whom we can call the representative agent. However, these problems are not standard, since both the evolution of the state and the objective functional is influenced but terms which are not directly related to the state or the control of the decision maker. They are however, indirectly related to him, in the sense that they model a very large community of agents similar to the representative agent. All the agents behave similarly and impact the representative agent. However, because of the large number an aggregation effect takes place. The interesting consequence is that the impact of the community can be modeled by a mean field term, but when this is done, the problem is reduced to a control problem. ​