الصفحة 1
الصفحة 1
Nonlinear Parabolic-Hyperbolic Coupled Systems and Their Attractors
This book presents recent results concerning the global existence in time, the large-time behaviour, decays of solutions and the existence of global attractors for some nonlinear parabolic-hyperbolic coupled systems of evolutionary partial differential equations arising from physics, mechanics and material science, such as the compressible Navier-Stokes equations, thermo(visco)elastic systems and elastic systems. To keep the book as self-contained as possible, the first chapter introduces to the needed results and tools from functional analysis, Sobolev spaces, differential and integral inequa.
Nonlinear Elliptic and Parabolic Problems : A Special Tribute to the Work of Herbert Amann
The present volume is dedicated to celebrate the work of the renowned mathematician Herbert Amann, who had a significant and decisive influence in shaping Nonlinear Analysis. Most articles published in this book, which consists of 32 articles in total, written by highly distinguished researchers, are in one way or another related to the scientific works of Herbert Amann. The contributions cover a wide range of nonlinear elliptic and parabolic equations with applications to natural sciences and engineering. Special topics are fluid dynamics, reaction-diffusion systems, bifurcation theory, maximal regularity, evolution equations, and the theory of function spaces.
Meshfree Methods for Partial Differential Equations II
A Particle Strategy for Solving the Fokker-Planck Equation Modelling the Fiber Orientation Distribution in Steady Recirculating Flows Involving Short Fiber Suspensions.- Extended Meshfree Method for Elastic and Inelastic Media.- Meshfree Petrov-Galerkin Methods for the Incompressible Navier-Stokes Equations.- The ?-shape Based Natural Element Method in Solid and Fluid Mechanics.- A Particle-Partition of Unity Method Part VI: A p-robust Multilevel Solver.- Enriched Reproducing Kernel Approximation: Reproducing Functions with Discontinuous Derivatives.- Reproducing Kernel Element Interpolation: Globally Conforming I m/C n/P k Hierarchies.- Multi-scale Analysis Using Two Influence Radii in EFGM.- Solution of a Dynamic Main Crack Interaction with a System of Micro-Cracks by the Element Free Galerkin Method.- Finite Cover Method for Physically and Geometrically Nonlinear Problems.- A Numerical Scheme for Solving Incompressible and Low Mach Number Flows by the Finite Pointset Method.- SPH Renormalized Hybrid Methods for Conservation Laws: Applications to Free Surface Flows.- Discontinuous Radial Basis Function Approximations for Meshfree Methods.- Treating Moving Interfaces in Thermal Models with the C-NEM.- Bridging Scale Particle and Finite Element Methods.
Mathematics of Large Eddy Simulation of Turbulent Flows
Large eddy simulation (LES) is a method of scientific computation seeking to predict the dynamics of organized structures in turbulent flows by approximating local, spatial averages of the flow. This book focuses on the mathematical foundations of LES and its models and provides a connection between the powerful tools of applied mathematics, partial differential equations and LES. Thus, it is concerned with fundamental aspects not treated so deeply in the other books in the field, aspects such as well-posedness of the models, their energy balance and the connection to the Leray theory of weak solutions of the Navier-Stokes equations.
Instability in Models Connected with Fluid Flows II
Instability in Models Connected with Fluid Flows II presents chapters from world renowned specialists. The stability of mathematical models simulating physical processes is discussed in topics on control theory, first order linear and nonlinear equations, water waves, free boundary problems, large time asymptotics of solutions, stochastic equations, Euler equations, Navier-Stokes equations, and other PDEs of fluid mechanics. Fields covered include: the free surface Euler (or water-wave) equations, the Cauchy problem for transport equations, irreducible Chapman--Enskog projections and Navier-Stokes approximations, randomly forced PDEs, stability of equilibrium figures of uniformly rotating viscous incompressible liquid, Navier-Stokes equations in cylindrical domains, Navier-Stokes-Poisson flows in a vacuum.
Instability in Models Connected with Fluid Flows I
Instability in Models Connected with Fluid Flows I presents chapters from world renowned specialists. The stability of mathematical models simulating physical processes is discussed in topics on control theory, first order linear and nonlinear equations, water waves, free boundary problems, large time asymptotics of solutions, stochastic equations, Euler equations, Navier-Stokes equations, and other PDEs of fluid mechanics. Fields covered include: controllability and accessibility properties of the Navier- Stokes and Euler systems, nonlinear dynamics of particle-like wavepackets, attractors of nonautonomous Navier-Stokes systems, large amplitude monophase nonlinear geometric optics, existence results for 3D Navier-Stokes equations and smoothness results for 2D Boussinesq equations, instability of incompressible Euler equations, increased stability in the Cauchy problem for elliptic equations.
Fluid Mechanics : An Introduction to the Theory of Fluid Flows
Advancements of fluid flow measuring techniques and of computational methods have led to new ways to treat laminar and turbulent flows. These methods are extensively used these days in research and engineering practise. This also requires new ways to teach the subject to students at higher educational institutions in an introductory manner. The book provides the knowledge to students in engineering and natural science needed to enter fluid mechanics applications in various fields. Analytical treatments are provided, based on the Navier-Stokes equations. Introductions are also given into numerical and experimental methods applied to flows. The main benefit the reader will derive from the book is a sound introduction into all aspects of fluid mechanics covering all relevant subfields.
Fluid and thermodynamics ; Vol.1 : Basic fluid mechanics
Simple, yet precise solutions to special flows are also constructed, namely Blasius boundary layer flows, matched asymptotics of the Navier-Stokes equations, global laws of steady and unsteady boundary layer flows and laminar and turbulent pipe flows
Control of Coupled Partial Differential Equations
Contains selected contributions originating from the ‘Conference on Optimal Control of Coupled Systems of Partial Differential Equations’, held at the ‘Mathematisches Forschungsinstitut Oberwolfach’ in April 2005.
Computational Fluid Dynamics for Wind Engineering
Covers topics such as: Fluid mechanics, turbulence in fluid mechanics, turbulence modelling, and mathematical modelling of wind engineering problems The finite difference method for CFD, solutions to the incompressible Navier-Stokes equations, visualization, and animation in CFD, and the application of CFD to building and bridge aerodynamics How to compare CFD analysis with wind tunnel measurements, field measurements, and the ASCE-7 pressure coefficients Wind effects and strain on large structures
Mathematical Foundation of Turbulent Viscous Flows : Lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, September 1-5, 2003
Five leading specialists reflect on different and complementary approaches to fundamental questions in the study of the Fluid Mechanics and Gas Dynamics equations. Constantin presents the Euler equations of ideal incompressible fluids and discusses the blow-up problem for the Navier-Stokes equations of viscous fluids, describing some of the major mathematical questions of turbulence theory.
IUTAM Symposium on Laminar-Turbulent Transition and Finite Amplitude Solutions
This volume contains refereed papers presented symposium on "Non-Uniqueness of Solutions to the Navier-Stokes equations and their Connection with Laminar-Turbulent Transition" The central objective of the symposium was to discuss the increasing amount of experimental and numerical evidence for finite amplitude solutions to the Navier-Stokes equations and to set the work into a modern theoretical context.
