Mathematical Analysis and Numerical Methods for Science and Technology

Released on by Robert Dautray
preview-18

  • Mathematical Analysis and Numerical Methods for Science and Technology Book Detail

  • Author : Robert Dautray
  • Release Date : 1999-11-23
  • Publisher : Springer Science & Business Media
  • Genre : Mathematics
  • Pages : 760
  • ISBN 13 : 9783540661016
  • File Size : 13,13 MB
DOWNLOAD BOOK

Mathematical Analysis and Numerical Methods for Science and Technology by Robert Dautray PDF Summary

Book Description: 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. The functional space framework used will be, for simplicity, a Banach space(3). To summarise, we wish to extend definition (2) for bounded operators A, i.e. G(t) = exp( - tA) , to unbounded operators A over X, where X is now a Banach space. Plan of the Chapter We shall see in this chapter that this enterprise is possible, that it gives us in addition to what is demanded above, some supplementary information in a number of areas: - a new 'explicit' expression of the solution; - the regularity of the solution taking into account some conditions on the given data (u , u1,f etc ... ) with the notion of a strong solution; o - asymptotic properties of the solutions. In order to treat these problems we go through the following stages: in § 1, we shall study the principal properties of operators of semigroups {G(t)} acting in the space X, particularly the existence of an upper exponential bound (in t) of the norm of G(t). In §2, we shall study the functions u E X for which t --+ G(t)u is differentiable.

Disclaimer: www.yourbookbest.com does not own Mathematical Analysis and Numerical Methods for Science and Technology books pdf, neither created or scanned. We just provide the link that is already available on the internet, public domain and in Google Drive. If any way it violates the law or has any issues, then kindly mail us via contact us page to request the removal of the link.