Author: Ariel Barton
Publisher: American Mathematical Soc.
ISBN: 0821887408
Category : Mathematics
Languages : en
Pages : 120
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Book Description
In this monograph the author investigates divergence-form elliptic partial differential equations in two-dimensional Lipschitz domains whose coefficient matrices have small (but possibly nonzero) imaginary parts and depend only on one of the two coordinates. He shows that for such operators, the Dirichlet problem with boundary data in $L^q$ can be solved for $q1$ small enough, and provide an endpoint result at $p=1$.
Author: David Gilbarg
Publisher: Springer Science & Business Media
ISBN: 9783540411604
Category : Mathematics
Languages : en
Pages : 544
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Book Description
This work aims to be of interest to those who have to work with differential equations and acts either as a reference or as a book to learn from. The authors have made the treatment self-contained.
Author: Boris N. Khoromskij
Publisher: Springer Science & Business Media
ISBN: 3642187773
Category : Mathematics
Languages : en
Pages : 304
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Book Description
During the last decade essential progress has been achieved in the analysis and implementation of multilevel/rnultigrid and domain decomposition methods to explore a variety of real world applications. An important trend in mod ern numerical simulations is the quick improvement of computer technology that leads to the well known paradigm (see, e. g. , [78,179]): high-performance computers make it indispensable to use numerical methods of almost linear complexity in the problem size N, to maintain an adequate scaling between the computing time and improved computer facilities as N increases. In the h-version of the finite element method (FEM), the multigrid iteration real izes an O(N) solver for elliptic differential equations in a domain n c IRd d with N = O(h- ) , where h is the mesh parameter. In the boundary ele ment method (BEM) , the traditional panel clustering, fast multi-pole and wavelet based methods as well as the modern hierarchical matrix techniques are known to provide the data-sparse approximations to the arising fully populated stiffness matrices with almost linear cost O(Nr log?Nr), where 1 d Nr = O(h - ) is the number of degrees of freedom associated with the boundary. The aim of this book is to introduce a wider audience to the use of a new class of efficient numerical methods of almost linear complexity for solving elliptic partial differential equations (PDEs) based on their reduction to the interface.
Author: Charles B. Morrey
Publisher: American Mathematical Soc.
ISBN: 0821814044
Category : Differential equations, Partial
Languages : en
Pages : 177
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Book Description
Author: Ya-Zhe Chen
Publisher: American Mathematical Soc.
ISBN: 0821819240
Category : Mathematics
Languages : en
Pages : 266
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Book Description
There are two parts to the book. In the first part, a complete introduction of various kinds of a priori estimate methods for the Dirichlet problem of second order elliptic partial differential equations is presented. In the second part, the existence and regularity theories of the Dirichlet problem for linear and nonlinear second order elliptic partial differential systems are introduced. The book features appropriate materials and is an excellent textbook for graduate students. The volume is also useful as a reference source for undergraduate mathematics majors, graduate students, professors, and scientists.
Author: Lucio Boccardo
Publisher: Walter de Gruyter
ISBN: 3110315424
Category : Mathematics
Languages : en
Pages : 204
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Book Description
Elliptic partial differential equations is one of the main and most active areas in mathematics. This book is devoted to the study of linear and nonlinear elliptic problems in divergence form, with the aim of providing classical results, as well as more recent developments about distributional solutions. For this reason this monograph is addressed to master's students, PhD students and anyone who wants to begin research in this mathematical field.
Author: Qing Han
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 164
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Book Description
Author: Florica C. Cîrstea
Publisher: American Mathematical Soc.
ISBN: 0821890220
Category : Mathematics
Languages : en
Pages : 97
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Book Description
In particular, for b = 1 and λ = 0, we find a sharp condition on h such that the origin is a removable singularity for all non-negative solutions of [[eqref]]one, thus addressing an open question of Vázquez and Véron.
Author: Kening Lu
Publisher: American Mathematical Soc.
ISBN: 0821884840
Category : Mathematics
Languages : en
Pages : 97
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Book Description
The authors prove that in systems undergoing Hopf bifurcations, the effects of periodic forcing can be amplified by the shearing in the system to create sustained chaotic behavior. Specifically, strange attractors with SRB measures are shown to exist. The analysis is carried out for infinite dimensional systems, and the results are applicable to partial differential equations. Application of the general results to a concrete equation, namely the Brusselator, is given.
Author: Robert J. Buckingham
Publisher: American Mathematical Soc.
ISBN: 0821885456
Category : Mathematics
Languages : en
Pages : 148
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Book Description
The authors study the Cauchy problem for the sine-Gordon equation in the semiclassical limit with pure-impulse initial data of sufficient strength to generate both high-frequency rotational motion near the peak of the impulse profile and also high-frequency librational motion in the tails. They show that for small times independent of the semiclassical scaling parameter, both types of motion are accurately described by explicit formulae involving elliptic functions. These formulae demonstrate consistency with predictions of Whitham's formal modulation theory in both the hyperbolic (modulationally stable) and elliptic (modulationally unstable) cases.
