MATHEMATICAL ANALYSIS AND NUMERICAL METHODS FOR SCIENCE AND TECHNOLOGY. - Volume 5, Evolution Problems I.pdf

MATHEMATICAL ANALYSIS AND NUMERICAL METHODS FOR SCIENCE AND TECHNOLOGY. - Volume 5, Evolution Problems I

Robert Dautray

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.

Mathematical Analysis and Numerical Methods for Science and Technology: Volume 5 Evolution Problems I Robert Dautray , Jacques-Louis Lions (auth.) 299 G(t), and to obtain the corresponding properties of its Laplace transform (called the resolvent of - A) R(p) = (A + pl)-l , whose existence is linked with the spectrum of A.

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MATHEMATICAL ANALYSIS AND NUMERICAL METHODS FOR SCIENCE AND TECHNOLOGY. - Volume 5, Evolution Problems I.pdf

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