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    STUDIA MATHEMATICA - Issue no. 4 / 2008  
         
  Article:   BOOK REVIEWS: VICTOR G. ZVYAGIN AND DMITRY A. VOROTNIKOV, TOPOLOGICAL APPROXIMATION METHODS FOR EVOLUTIONARY PROBLEMS OF NONLINEAR HYDRODYNAMICS, WALTER DE GRUYTER, BERLIN 2008, XII+ 230 PP, ISBN 978-3-11-020222-9, ISSN 0941-813X.

Authors:  MIRELA KOHR.
 
       
         
  Abstract:  There are several methods to solve the evolutionary problems of fluid dynamics as the Faedo-Galerkin method, the iteration method, the method of evolutionary equations, and others. The authors of the present book propose another approach, based on the interpretation of the initial-boundary value problem as an operator equation in some appropriate function space. Usually the maps involved in this equation do not posses good operator properties, so that one approximates the initial equation by smoothing the nonlinear terms, or adding terms of higher order with a small parameter, allowing the study of this approximating equation in spaces with more suitable topological properties and the use of various discretization method with guaranteed convergence. The final step consists in passing to limit in the approximating equation, by letting the parameters to tend to 0 to find a solution of the original equation (usually in a topology weaker than that of the spaces where the approximating equation was studied).  
         
     
         
         
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