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Spatial Patterns

Spatial Patterns Author L.A. Peletier
ISBN-10 9781461201359
Release 2012-12-06
Pages 343
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The study of spatial patterns in extended systems, and their evolution with time, poses challenging questions for physicists and mathematicians alike. Waves on water, pulses in optical fibers, periodic structures in alloys, folds in rock formations, and cloud patterns in the sky: patterns are omnipresent in the world around us. Their variety and complexity make them a rich area of study. In the study of these phenomena an important role is played by well-chosen model equations, which are often simpler than the full equations describing the physical or biological system, but still capture its essential features. Through a thorough analysis of these model equations one hopes to glean a better under standing of the underlying mechanisms that are responsible for the formation and evolution of complex patterns. Classical model equations have typically been second-order partial differential equations. As an example we mention the widely studied Fisher-Kolmogorov or Allen-Cahn equation, originally proposed in 1937 as a model for the interaction of dispersal and fitness in biological populations. As another example we mention the Burgers equation, proposed in 1939 to study the interaction of diffusion and nonlinear convection in an attempt to understand the phenomenon of turbulence. Both of these are nonlinear second-order diffusion equations.



Multi pulse Evolution and Space time Chaos in Dissipative Systems

Multi pulse Evolution and Space time Chaos in Dissipative Systems Author Sergey Zelik
ISBN-10 9780821842645
Release 2009-03-06
Pages 97
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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.



A Study of Heteroclinic Orbits for a Class of Fourth Order Ordinary Differential Equations

A Study of Heteroclinic Orbits for a Class of Fourth Order Ordinary Differential Equations Author Denis Bonheure
ISBN-10 9782930344751
Release 2004-01-01
Pages 217
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In qualitative theory of differential equations, an important role is played by special classes of solutions, like periodic solutions or solutions to some boundary value problems. When a system of ordinary differential equations has equilibria, i.e. constant solutions, whose stability properties are known, it is significant to search for connections between them by trajectories of solutions of the given system. These are called homoclinic or heteroclinic, according to whether they describe a loop based at one single equilibrium or they "start" and "end" at two distinct equilibria. This thesis is devoted to the study of heteroclinic solutions for a specific class of ordinary differential equations related to the Extended Fisher-Kolmogorov equation and the Swift-Hohenberg equation. These are semilinear fourth order bi-stable evolution equations which appear as mathematical models for problems arising in Mechanics, Chemistry and Biology. For such equations, the set of bounded stationary solutions is of great interest. These solve an autonomous fourth order equation. In this thesis, we focus on such equations having a variational structure. In that case, the solutions are critical points of an associated action functional defined in convenient functional spaces. We then look for heteroclinic solutions as minimizers of the action functional. Our main contributions concern existence and multiplicity results of such global and local minimizers in the case where the functional is defined from sign changing Lagrangians. The underlying idea is to impose conditions which imply a lower bound on the action over all admissible functions. We then combine classical arguments of the Calculus of Variations with careful estimates on minimizing sequences to prove the existence of a minimum.



Handbook of Differential Equations Evolutionary Equations

Handbook of Differential Equations  Evolutionary Equations Author C.M. Dafermos
ISBN-10 0080931979
Release 2008-10-06
Pages 608
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The material collected in this volume discusses the present as well as expected future directions of development of the field with particular emphasis on applications. The seven survey articles present different topics in Evolutionary PDE’s, written by leading experts. - Review of new results in the area - Continuation of previous volumes in the handbook series covering Evolutionary PDEs - Written by leading experts



Mathematics Today

Mathematics Today Author
ISBN-10 UOM:39015072631792
Release 2007
Pages
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Mathematics Today has been writing in one form or another for most of life. You can find so many inspiration from Mathematics Today also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Mathematics Today book for free.



Advances in Differential Equations

Advances in Differential Equations Author
ISBN-10 UOM:39015059085368
Release 2004
Pages
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Advances in Differential Equations has been writing in one form or another for most of life. You can find so many inspiration from Advances in Differential Equations also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Advances in Differential Equations book for free.



Partial Differential Equations and Mathematical Physics

Partial Differential Equations and Mathematical Physics Author Kunihiko Kajitani
ISBN-10 UCSD:31822031960016
Release 2003
Pages 238
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Partial Differential Equations and Mathematical Physics has been writing in one form or another for most of life. You can find so many inspiration from Partial Differential Equations and Mathematical Physics also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Partial Differential Equations and Mathematical Physics book for free.



Mathematical Reviews

Mathematical Reviews Author
ISBN-10 UVA:X006180726
Release 2004
Pages
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Mathematical Reviews has been writing in one form or another for most of life. You can find so many inspiration from Mathematical Reviews also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Mathematical Reviews book for free.



Variational and Topological Methods in the Study of Nonlinear Phenomena

Variational and Topological Methods in the Study of Nonlinear Phenomena Author Vieri Benci
ISBN-10 UOM:39015054149623
Release 2002
Pages 131
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This volume covers recent advances in the field of nonlinear functional analysis and its applications to nonlinear partial and ordinary differential equations, with particular emphasis on variational and topological methods.A broad range of topics is covered, including: * concentration phenomena in pdes* variational methods with applications to pdes and physics* periodic solutions of odes* computational aspects in topological methods* mathematical models in biologyThough well-differentiated, the topics covered are unified through a common perspective and approach. Unique to the work are several chapters on computational aspects and applications to biology, not usually found with such basic studies on pdes and odes. The volume will be an excellent reference text for researchers and graduate students in the above mentioned fields.Contributors: M. Clapp, M. Del Pino, M. Esteban, P. Felmer, A. Ioffe, W. Marzantowicz, M. Mrozek, M. Musso, R. Ortega, P. Pilarczyk, E. Sere, P. Sintzoff, R. Turner, M. Willem



Energy Methods for Free Boundary Problems

Energy Methods for Free Boundary Problems Author Stanislav Nikolaevich Antont︠s︡ev
ISBN-10 UOM:39015053541721
Release 2002
Pages 329
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Energy Methods for Free Boundary Problems has been writing in one form or another for most of life. You can find so many inspiration from Energy Methods for Free Boundary Problems also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Energy Methods for Free Boundary Problems book for free.



Das Schweizer Buch

Das Schweizer Buch Author
ISBN-10 UOM:39015065126453
Release 2001
Pages
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Das Schweizer Buch has been writing in one form or another for most of life. You can find so many inspiration from Das Schweizer Buch also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Das Schweizer Buch book for free.



Introduction to Nonlinear Differential and Integral Equations

Introduction to Nonlinear Differential and Integral Equations Author Harold Thayer Davis
ISBN-10 0486609715
Release 1962
Pages 566
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Topics covered include differential equations of the 1st order, the Riccati equation and existence theorems, 2nd order equations, elliptic integrals and functions, nonlinear mechanics, nonlinear integral equations, more. Includes 137 problems.



Nonlinear Dynamics

Nonlinear Dynamics Author Muthusamy Lakshmanan
ISBN-10 9783642556883
Release 2012-12-06
Pages 620
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This self-contained treatment covers all aspects of nonlinear dynamics, from fundamentals to recent developments, in a unified and comprehensive way. Numerous examples and exercises will help the student to assimilate and apply the techniques presented.



Philosophy of Complex Systems

Philosophy of Complex Systems Author
ISBN-10 0080931227
Release 2011-05-23
Pages 952
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The domain of nonlinear dynamical systems and its mathematical underpinnings has been developing exponentially for a century, the last 35 years seeing an outpouring of new ideas and applications and a concomitant confluence with ideas of complex systems and their applications from irreversible thermodynamics. A few examples are in meteorology, ecological dynamics, and social and economic dynamics. These new ideas have profound implications for our understanding and practice in domains involving complexity, predictability and determinism, equilibrium, control, planning, individuality, responsibility and so on. Our intention is to draw together in this volume, we believe for the first time, a comprehensive picture of the manifold philosophically interesting impacts of recent developments in understanding nonlinear systems and the unique aspects of their complexity. The book will focus specifically on the philosophical concepts, principles, judgments and problems distinctly raised by work in the domain of complex nonlinear dynamical systems, especially in recent years. -Comprehensive coverage of all main theories in the philosophy of Complex Systems -Clearly written expositions of fundamental ideas and concepts -Definitive discussions by leading researchers in the field -Summaries of leading-edge research in related fields are also included



Lecture Notes in Applied Differential Equations of Mathematical Physics

Lecture Notes in Applied Differential Equations of Mathematical Physics Author Luiz C. L. Botelho
ISBN-10 9789812814579
Release 2008
Pages 324
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Functional analysis is a well-established powerful method in mathematical physics, especially those mathematical methods used in modern non-perturbative quantum field theory and statistical turbulence. This book presents a unique, modern treatment of solutions to fractional random differential equations in mathematical physics. It follows an analytic approach in applied functional analysis for functional integration in quantum physics and stochastic Langevin?turbulent partial differential equations.



Theoretical and Applied Mechanics

Theoretical and Applied Mechanics Author Frithiof I. Niordson
ISBN-10 9781483221069
Release 2013-10-15
Pages 470
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Theoretical and Applied Mechanics covers the proceedings of the 16th International Congress of Theoretical and Applied Mechanics, held at the Technical University of Denmark, Lyngby, Denmark on August 19-25, 1984. The contributors consider the significant advances in the thriving field of mechanics. This book is composed of 21 chapters, and begins with an overview of space research contributions in understanding fluid media mechanics. This topic is followed by discussions on some aspects and fundamentals of mechanics, such as chaos, computer application, resonant phenomena, adiabaticity, and nonlinear acoustics. The following chapters explore the various applications of theoretical and applied mechanics, including in marine structures, oil recovery, and ice and snow mechanics. This book also deals with nonlinear wave motion, hydrodynamic systems, ocean wave spectra, and Helmholtz concept. The remaining chapters look into the issues of steady water bifurcation, concept of anisotropic soils, and flow visualization. This book is of great value to physicists and research workers who wish to expand their knowledge in mechanics.



Classical Methods in Ordinary Differential Equations

Classical Methods in Ordinary Differential Equations Author Stuart P. Hastings
ISBN-10 9780821846940
Release 2011-12-15
Pages 373
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This text emphasizes rigorous mathematical techniques for the analysis of boundary value problems for ODEs arising in applications. The emphasis is on proving existence of solutions, but there is also a substantial chapter on uniqueness and multiplicity questions and several chapters which deal with the asymptotic behavior of solutions with respect to either the independent variable or some parameter. These equations may give special solutions of important PDEs, such as steady state or traveling wave solutions. Often two, or even three, approaches to the same problem are described. The advantages and disadvantages of different methods are discussed. The book gives complete classical proofs, while also emphasizing the importance of modern methods, especially when extensions to infinite dimensional settings are needed. There are some new results as well as new and improved proofs of known theorems. The final chapter presents three unsolved problems which have received much attention over the years. Both graduate students and more experienced researchers will be interested in the power of classical methods for problems which have also been studied with more abstract techniques. The presentation should be more accessible to mathematically inclined researchers from other areas of science and engineering than most graduate texts in mathematics.