Long Time Behavior Of Second Order Evolution Equations With Nonlinear Damping

Author : I. Lasiecka, Igor Chueshov
Publisher : American Mathematical Soc.
ISBN 13 : 9780821866535
Total Pages : 204 pages
Book Rating : 4.32/5 ( download)

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Download or read book Long-Time Behavior of Second Order Evolution Equations with Nonlinear Damping written by I. Lasiecka, Igor Chueshov and published by American Mathematical Soc.. This book was released on 2008-08-08 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors consider abstract nonlinear second order evolution equations with a nonlinear damping. Questions related to long time behavior, existence and structure of global attractors are studied. Particular emphasis is put on dynamics which--in addition to nonlinear dissipation-- have noncompact semilinear terms and whose energy may not be necessarily decreasing. For such systems the authors first develop a general theory at the abstract level. They then apply the general theory to nonlinear wave and plate equations exhibiting the aforementioned characteristics and are able to provide new results pertaining to several open problems in the area of structure and properties of global attractors arising in this class of PDE dynamics.

Author : Igor Chueshov
Publisher : American Mathematical Soc.
ISBN 13 : 0821841874
Total Pages : 200 pages
Book Rating : 4.77/5 ( download)

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Download or read book Long-Time Behavior of Second Order Evolution Equations with Nonlinear Damping written by Igor Chueshov and published by American Mathematical Soc.. This book was released on 2008 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors consider abstract nonlinear second order evolution equations with a nonlinear damping. Questions related to long time behavior, existence and structure of global attractors are studied. Particular emphasis is put on dynamics which--in addition to nonlinear dissipation-- have noncompact semilinear terms and whose energy may not be necessarily decreasing. For such systems the authors first develop a general theory at the abstract level. They then apply the general theoryto nonlinear wave and plate equations exhibiting the aforementioned characteristics and are able to provide new results pertaining to several open problems in the area of structure and properties of global attractors arising in this class of PDE dynamics.

Author : Igor Chueshov
Publisher : Springer Science & Business Media
ISBN 13 : 0387877126
Total Pages : 777 pages
Book Rating : 4.29/5 ( download)

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Download or read book Von Karman Evolution Equations written by Igor Chueshov and published by Springer Science & Business Media. This book was released on 2010-04-08 with total page 777 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the study of mathematical models that arise in the context of concrete - plications, the following two questions are of fundamental importance: (i) we- posedness of the model, including existence and uniqueness of solutions; and (ii) qualitative properties of solutions. A positive answer to the ?rst question, - ing of prime interest on purely mathematical grounds, also provides an important test of the viability of the model as a description of a given physical phenomenon. An answer or insight to the second question provides a wealth of information about the model, hence about the process it describes. Of particular interest are questions related to long-time behavior of solutions. Such an evolution property cannot be v- i?ed empirically, thus any in a-priori information about the long-time asymptotics can be used in predicting an ultimate long-time response and dynamical behavior of solutions. In recent years, this set of investigations has attracted a great deal of attention. Consequent efforts have then resulted in the creation and infusion of new methods and new tools that have been responsible for carrying out a successful an- ysis of long-time behavior of several classes of nonlinear PDEs.

Author : Alain Haraux
Publisher : Springer
ISBN 13 : 331978515X
Total Pages : 102 pages
Book Rating : 4.58/5 ( download)

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Download or read book Nonlinear Vibrations and the Wave Equation written by Alain Haraux and published by Springer. This book was released on 2018-05-02 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gathers the revised lecture notes from a seminar course offered at the Federal University of Rio de Janeiro in 1986, then in Tokyo in 1987. An additional chapter has been added to reflect more recent advances in the field.

Author : Kaïs Ammari
Publisher : Cambridge University Press
ISBN 13 : 1108412300
Total Pages : 205 pages
Book Rating : 4.08/5 ( download)

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Download or read book Evolution Equations written by Kaïs Ammari and published by Cambridge University Press. This book was released on 2018 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: The proceedings of a summer school held in 2015 whose theme was long time behavior and control of evolution equations.

Author : Tomáš Bodnár
Publisher : Springer Nature
ISBN 13 : 3031473558
Total Pages : 376 pages
Book Rating : 4.55/5 ( download)

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Download or read book Fluids Under Control written by Tomáš Bodnár and published by Springer Nature. This book was released on with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Salah-Eldin Mohammed
Publisher : American Mathematical Soc.
ISBN 13 : 0821842501
Total Pages : 120 pages
Book Rating : 4.08/5 ( download)

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Download or read book The Stable Manifold Theorem for Semilinear Stochastic Evolution Equations and Stochastic Partial Differential Equations written by Salah-Eldin Mohammed and published by American Mathematical Soc.. This book was released on 2008 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main objective of this paper is to characterize the pathwise local structure of solutions of semilinear stochastic evolution equations and stochastic partial differential equations near stationary solutions.

Author : Victor A. Sadovnichiy
Publisher : Springer Nature
ISBN 13 : 303050302X
Total Pages : 525 pages
Book Rating : 4.24/5 ( download)

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Download or read book Contemporary Approaches and Methods in Fundamental Mathematics and Mechanics written by Victor A. Sadovnichiy and published by Springer Nature. This book was released on 2020-11-24 with total page 525 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the latest approaches and methods in fundamental mathematics and mechanics, and discusses the practical application of abstract mathematical approaches, such as differential geometry, and differential and difference equations in solid mechanics, hydrodynamics, aerodynamics, optimization, decision-making theory and control theory. Featuring selected contributions to the open seminar series of Lomonosov Moscow State University and Igor Sikorsky Kyiv Polytechnic Institute by mathematicians from China, Germany, France, Italy, Spain, Russia, Ukraine and the USA, the book will appeal to mathematicians and engineers working at the interface of these fields

Author : Sergey Zelik
Publisher : American Mathematical Soc.
ISBN 13 : 0821842641
Total Pages : 112 pages
Book Rating : 4.45/5 ( download)

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Download or read book Multi-Pulse Evolution and Space-Time Chaos in Dissipative Systems written by Sergey Zelik and published by American Mathematical Soc.. This book was released on 2009-03-06 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors study semilinear parabolic systems on the full space ${\mathbb R}^n$ that admit a family of exponentially decaying pulse-like steady states obtained via translations. The multi-pulse solutions under consideration look like the sum of infinitely many such pulses which are well separated. They prove a global center-manifold reduction theorem for the temporal evolution of such multi-pulse solutions and show that the dynamics of these solutions can be described by an infinite system of ODEs for the positions of the pulses. As an application of the developed theory, The authors verify the existence of Sinai-Bunimovich space-time chaos in 1D space-time periodically forced Swift-Hohenberg equation.

Author : Sergiu Aizicovici
Publisher : American Mathematical Soc.
ISBN 13 : 0821841920
Total Pages : 84 pages
Book Rating : 4.21/5 ( download)

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Download or read book Degree Theory for Operators of Monotone Type and Nonlinear Elliptic Equations with Inequality Constraints written by Sergiu Aizicovici and published by American Mathematical Soc.. This book was released on 2008 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper the authors examine the degree map of multivalued perturbations of nonlinear operators of monotone type and prove that at a local minimizer of the corresponding Euler functional, this degree equals one.