Mathematical Analysis and Numerical Methods fos Science and Technology - Volume 6, Evolution Problems II

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Robert Dautray et Jacques-Louis Lions - Mathematical Analysis and Numerical Methods fos Science and Technology - Volume 6, Evolution Problems II.
Volumes 5 and 6 examine evolution (i.e. time-dependent) problems. The methods presented are useful for physics and mechanics (Chapter XV) as well as electronics,... Lire la suite
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Résumé

Volumes 5 and 6 examine evolution (i.e. time-dependent) problems. The methods presented are useful for physics and mechanics (Chapter XV) as well as electronics, automata theory and robotics, etc. (Chapter XVI). In Chapter XVII it is shown that for a large class of problems the solution may be expressed in terms of a family (or semi-group) of time-dependent operators. Chapter XVIII deals with variational methods which are the simplest and the most powerful methods applicable to both non-symmetric and time-dependent operators, and form a basis for the study of nonlinear problems. The linearised Navier-Stokes equations are considered in Chapter XIX with particular variational methods. Chapter XX presents the methods of computation for evolution problems, serving as a basis for the effective calculation of evolutions on computer. The final chapter presents the many important and specific properties of the operator of transport equations.

Sommaire

  • THE LINEARISED NAVIER-STOKES EQUATIONS
    • The Stationary Navier-Stokes Equations: The Linear Case
    • The Evolutionary Navier-Stokes Equations : The Linear Case
    • Additional Results and Review
  • NUMERICAL METHODS FOR EVOLUTION PROBLEMS
    • Problems of First Order in Time
    • Problems of Second Order in Time
    • The Advection Equation
    • Symmetric Friedrichs Systems
    • The Transport Equation
    • Numerical Solution of the Stokes Problem
  • TRANSPORT
    • Presentation of Physical Problems
    • Existence and Uniqueness of Solutions of the Transport Equation
    • Spectral Theory and Asymptotic Behaviour of the Solutions of Evolution Problems
    • Explicit Examples
    • Approximation of the Neutron Transport Equation by the Diffusion Equation.

Caractéristiques

  • Date de parution
    01/12/1999
  • Editeur
  • ISBN
    3-540-66102-6
  • EAN
    9783540661023
  • Présentation
    Broché
  • Nb. de pages
    485 pages
  • Poids
    0.64 Kg
  • Dimensions
    15,5 cm × 23,4 cm × 2,5 cm

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