Equadiff 95 - Proceedings Of The International Conference On Differential Equations


Author: Magalhaes L,Rocha Carlos,Sanchez L

Publisher: World Scientific

ISBN: 9814545074


Page: 576

View: 1965

In this volume, leading experts on differential equations address recent advances in the fields of ordinary differential equations and dynamical systems, partial differential equations and calculus of variations, and their related applications.

Spectral Theory for Random and Nonautonomous Parabolic Equations and Applications


Author: Janusz Mierczynski,Wenxian Shen

Publisher: CRC Press

ISBN: 9781584888963

Category: Mathematics

Page: 336

View: 2153

Providing a basic tool for studying nonlinear problems, Spectral Theory for Random and Nonautonomous Parabolic Equations and Applications focuses on the principal spectral theory for general time-dependent and random parabolic equations and systems. The text contains many new results and considers existing results from a fresh perspective. Taking a clear, unified, and self-contained approach, the authors first develop the abstract general theory in the framework of weak solutions, before turning to cases of random and nonautonomous equations. They prove that time dependence and randomness do not reduce the principal spectrum and Lyapunov exponents of nonautonomous and random parabolic equations. The book also addresses classical Faber–Krahn inequalities for elliptic and time-periodic problems and extends the linear theory for scalar nonautonomous and random parabolic equations to cooperative systems. The final chapter presents applications to Kolmogorov systems of parabolic equations. By thoroughly explaining the spectral theory for nonautonomous and random linear parabolic equations, this resource reveals the importance of the theory in examining nonlinear problems.

Topological Methods in Differential Equations and Inclusions


Author: Andrzej Granas,Marlène Frigon

Publisher: Springer Science & Business Media

ISBN: 9401103399

Category: Mathematics

Page: 522

View: 1667

The papers collected in this volume are contributions to the 33rd session of the Seminaire de Mathematiques Superieures (SMS) on "Topological Methods in Differential Equations and Inclusions". This session of the SMS took place at the Universite de Montreal in July 1994 and was a NATO Advanced Study Institute (ASI). The aim of the ASI was to bring together a considerable group of young researchers from various parts of the world and to present to them coherent surveys of some of the most recent advances in this area of Nonlinear Analysis. During the meeting 89 mathematicians from 20 countries have had the opportunity to get acquainted with various aspects of the subjects treated in the lectures as well as the chance to exchange ideas and learn about new problems arising in the field. The main topics teated in this ASI were the following: Fixed point theory for single- and multi-valued mappings including topological degree and its generalizations, and topological transversality theory; existence and multiplicity results for ordinary differential equations and inclusions; bifurcation and stability problems; ordinary differential equations in Banach spaces; second order differential equations on manifolds; the topological structure of the solution set of differential inclusions; effects of delay perturbations on dynamics of retarded delay differential equations; dynamics of reaction diffusion equations; non smooth critical point theory and applications to boundary value problems for quasilinear elliptic equations.

Shadowing in Dynamical Systems

Theory and Applications


Author: K.J. Palmer

Publisher: Springer Science & Business Media

ISBN: 9780792361794

Category: Mathematics

Page: 300

View: 7632

In this book the theory of hyperbolic sets is developed, both for diffeomorphisms and flows, with an emphasis on shadowing. We show that hyperbolic sets are expansive and have the shadowing property. Then we use shadowing to prove that hyperbolic sets are robust under perturbation, that they have an asymptotic phase property and also that the dynamics near a transversal homoclinic orbit is chaotic. It turns out that chaotic dynamical systems arising in practice are not quite hyperbolic. However, they possess enough hyperbolicity to enable us to use shadowing ideas to give computer-assisted proofs that computed orbits of such systems can be shadowed by true orbits for long periods of time, that they possess periodic orbits of long periods and that it is really true that they are chaotic. Audience: This book is intended primarily for research workers in dynamical systems but could also be used in an advanced graduate course taken by students familiar with calculus in Banach spaces and with the basic existence theory for ordinary differential equations.

Nonlinear Phenomena in Mathematical Sciences

Proceedings of an International Conference on Nonlinear Phenomena in Mathematical Sciences, Held at the University of Texas at Arlington, Arlington, Texas, June 16–20, 1980


Author: V. Lakshmikantham

Publisher: Elsevier

ISBN: 1483272052

Category: Mathematics

Page: 1062

View: 6520

Nonlinear Phenomena in Mathematical Sciences contains the proceedings of an International Conference on Nonlinear Phenomena in Mathematical Sciences, held at the University of Texas at Arlington, on June 16-20,1980. The papers explore trends in nonlinear phenomena in mathematical sciences, with emphasis on nonlinear functional analytic methods and their applications; nonlinear wave theory; and applications to medical and life sciences. In the area of nonlinear functional analytic methods and their applications, the following subjects are discussed: optimal control theory; periodic oscillations of nonlinear mechanical systems; Leray-Schauder degree theory; differential inequalities applied to parabolic and elliptic partial differential equations; bifurcation theory, stability theory in analytical mechanics; singular and ordinary boundary value problems, etc. The following topics in nonlinear wave theory are considered: nonlinear wave propagation in a randomly homogeneous media; periodic solutions of a semilinear wave equation; asymptotic behavior of solutions of strongly damped nonlinear wave equations; shock waves and dissipation theoretical methods for a nonlinear Schr?dinger equation; and nonlinear hyperbolic Volterra equations occurring in viscoelasticity. Applications to medical and life sciences include mathematical modeling in physiology, pharmacokinetics, and neuro-mathematics, along with epidemic modeling and parameter estimation techniques. This book will be helpful to students, practitioners, and researchers in the field of mathematics.

Hamiltonian Dynamical Systems and Applications


Author: Walter Craig

Publisher: Springer Science & Business Media

ISBN: 1402069642

Category: Mathematics

Page: 441

View: 1419

This volume is the collected and extended notes from the lectures on Hamiltonian dynamical systems and their applications that were given at the NATO Advanced Study Institute in Montreal in 2007. Many aspects of the modern theory of the subject were covered at this event, including low dimensional problems. Applications are also presented to several important areas of research, including problems in classical mechanics, continuum mechanics, and partial differential equations.

Modeling Atmospheric and Oceanic Flows

Insights from Laboratory Experiments and Numerical Simulations


Author: Thomas von Larcher,Paul D. Williams

Publisher: John Wiley & Sons

ISBN: 1118855922

Category: Science

Page: 368

View: 7191

Modeling Atmospheric and Oceanic Flows: Insights from LaboratoryExperiments and Numerical Simulations provides a broad overview ofrecent progress in using laboratory experiments and numericalsimulations to model atmospheric and oceanic fluid motions. Thisvolume not only surveys novel research topics in laboratoryexperimentation, but also highlights recent developments in thecorresponding computational simulations. As computing power growsexponentially and better numerical codes are developed, theinterplay between numerical simulations and laboratory experimentsis gaining paramount importance within the scientific community.The lessons learnt from the laboratory–model comparisons inthis volume will act as a source of inspiration for the nextgeneration of experiments and simulations. Volume highlightsinclude: Topics pertaining to atmospheric science, climatephysics, physical oceanography, marine geology and geophysics Overview of the most advanced experimental andcomputational research in geophysics Recent developments in numerical simulations ofatmospheric and oceanic fluid motion Unique comparative analysis of the experimentaland numerical approaches to modeling fluid flow Modeling Atmospheric and Oceanic Flows will be a valuableresource for graduate students, researchers, and professionals inthe fields of geophysics, atmospheric sciences, oceanography,climate science, hydrology, and experimental geosciences.



Author: N.A

Publisher: N.A


Category: Mathematics

Page: N.A

View: 9428

Mean Field Theories and Dual Variation


Author: Takashi Suzuki

Publisher: Atlantis Press

ISBN: 9789078677147

Category: Mathematics

Page: 288

View: 9362

A mathematical theory is introduced in this book to unify a large class of nonlinear partial differential equation (PDE) models for better understanding and analysis of the physical and biological phenomena they represent. The so-called mean field approximation approach is adopted to describe the macroscopic phenomena from certain microscopic principles for this unified mathematical formulation. Two key ingredients for this approach are the notions of "duality" according to the PDE weak solutions and "hierarchy" for revealing the details of the otherwise hidden secrets, such as physical mystery hidden between particle density and field concentration, quantized blow up biological mechanism sealed in chemotaxis systems, as well as multi-scale mathematical explanations of the Smoluchowski Poisson model in non-equilibrium thermodynamics, two-dimensional turbulence theory, self-dual gauge theory, and so forth. This book shows how and why many different nonlinear problems are inter-connected in terms of the properties of duality and scaling, and the way to analyze them mathematically.