Partielle Differentialgleichungen

Eine anwendungsorientierte Einführung


Author: Ben Schweizer

Publisher: Springer-Verlag

ISBN: 3662566680

Category: Mathematics

Page: 585

View: 6146

Das Buch führt in die Theorie der Partiellen Differentialgleichungen ein, lediglich die Grundvorlesungen der Analysis werden vorausgesetzt. Eine Vielzahl linearer und nichtlinearer Differentialgleichungen wird mit Modellierungsansätzen motiviert und rigoros analysiert. Nach den klassischen linearen Problemen der Potentialtheorie und Wärmeleitung werden insbesondere nichtlineare Probleme aus der Theorie poröser Medien, der Strömungsmechanik und der Festkörpermechanik behandelt. Entlang der Aufgabenstellungen von zunehmender Komplexität werden moderne Methoden und Theorien der Analysis entwickelt.​ In der vorliegenden 2. Auflage ist der Text überarbeitet und korrigiert, viele Zeichnungen sind verbessert, Anhang und Index sind erweitert.

Dynamics Reported

A Series in Dynamical Systems and Their Applications


Author: Urs Kirchgraber,Hans Otto Walther

Publisher: Springer-Verlag

ISBN: 3322966577

Category: Science

Page: 269

View: 7195

Mathematik der Selbstorganisation

Qualitative Theorie nichtlinearer dynamischer Systeme und gleichgewichtsferner Strukturen in Physik, Chemie und Biologie


Author: Gottfried Jetschke

Publisher: Springer-Verlag

ISBN: 3322859185

Category: Science

Page: 333

View: 5649

Shadowing in Dynamical Systems

Theory and Applications


Author: K.J. Palmer

Publisher: Springer Science & Business Media

ISBN: 9780792361794

Category: Mathematics

Page: 300

View: 7445

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.

Hamiltonian Dynamical Systems and Applications


Author: Walter Craig

Publisher: Springer Science & Business Media

ISBN: 1402069642

Category: Mathematics

Page: 441

View: 545

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: 6890

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: 2937

Mean Field Theories and Dual Variation


Author: Takashi Suzuki

Publisher: Atlantis Press

ISBN: 9789078677147

Category: Mathematics

Page: 288

View: 1294

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.

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: 9179

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.