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Author: Igor Chueshov
Publisher: American Mathematical Soc.
ISBN: 0821841874
Category : Mathematics
Languages : en
Pages : 200
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Book Description
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: American Mathematical Soc.
ISBN: 0821841874
Category : Mathematics
Languages : en
Pages : 200
Get Book Here
Book Description
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: I. Lasiecka, Igor Chueshov
Publisher: American Mathematical Soc.
ISBN: 9780821866535
Category :
Languages : en
Pages : 204
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Book Description
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: Springer Science & Business Media
ISBN: 0387877126
Category : Mathematics
Languages : en
Pages : 777
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Book Description
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: Richard F. Bass
Publisher: American Mathematical Soc.
ISBN: 0821842870
Category : Mathematics
Languages : en
Pages : 98
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Book Description
Given a symmetric random walk in ${\mathbb Z}^2$ with finite second moments, let $R_n$ be the range of the random walk up to time $n$. The authors study moderate deviations for $R_n -{\mathbb E}R_n$ and ${\mathbb E}R_n -R_n$. They also derive the corresponding laws of the iterated logarithm.
Author: Ulrich Bunke
Publisher: American Mathematical Soc.
ISBN: 0821842846
Category : Mathematics
Languages : en
Pages : 134
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Book Description
This paper sets up a language to deal with Dirac operators on manifolds with corners of arbitrary codimension. In particular the author develops a precise theory of boundary reductions. The author introduces the notion of a taming of a Dirac operator as an invertible perturbation by a smoothing operator. Given a Dirac operator on a manifold with boundary faces the author uses the tamings of its boundary reductions in order to turn the operator into a Fredholm operator. Its index is an obstruction against extending the taming from the boundary to the interior. In this way he develops an inductive procedure to associate Fredholm operators to Dirac operators on manifolds with corners and develops the associated obstruction theory.
Author: Pierre Magal
Publisher: American Mathematical Soc.
ISBN: 0821846531
Category : Mathematics
Languages : en
Pages : 84
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Book Description
Several types of differential equations, such as delay differential equations, age-structure models in population dynamics, evolution equations with boundary conditions, can be written as semilinear Cauchy problems with an operator which is not densely defined in its domain. The goal of this paper is to develop a center manifold theory for semilinear Cauchy problems with non-dense domain. Using Liapunov-Perron method and following the techniques of Vanderbauwhede et al. in treating infinite dimensional systems, the authors study the existence and smoothness of center manifolds for semilinear Cauchy problems with non-dense domain. As an application, they use the center manifold theorem to establish a Hopf bifurcation theorem for age structured models.
Author: Huaxin Lin
Publisher: American Mathematical Soc.
ISBN: 0821851942
Category : Mathematics
Languages : en
Pages : 144
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Book Description
"Volume 205, number 963 (second of 5 numbers)."
Author: Adam Coffman
Publisher: American Mathematical Soc.
ISBN: 0821846574
Category : Mathematics
Languages : en
Pages : 105
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Book Description
"Volume 205, number 962 (first of 5 numbers)."
Author: Michael Thoreau Lacey
Publisher: American Mathematical Soc.
ISBN: 0821845403
Category : Mathematics
Languages : en
Pages : 87
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Book Description
"Volume 205, number 965 (fourth of 5 numbers)."
Author: Gelu Popescu
Publisher: American Mathematical Soc.
ISBN: 0821847104
Category : Mathematics
Languages : en
Pages : 137
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Book Description
"Volume 205, number 964 (third of 5 numbers)."
