Mathematical Analysis And Numerical Methods For Science And Technology: Volume 5 Evolution Problems I

Mathematical Analysis And Numerical Methods For Science And Technology: Volume 5 Evolution Problems I

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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.

  • Used Book in Good Condition
Author

Robert Dautray

Author

Jacques-Louis Lions

Binding

Paperback

Brand

Brand: Springer

Creator

A. Craig

Creator

M. Artola

Creator

M. Cessenat

Creator

H. Lanchon

EAN

9783540661016

ISBN

3540661018

Label

Springer

Manufacturer

Springer

NumberOfPages

739

ProductGroup

Book

ProductTypeName

ABIS_BOOK

PublicationDate

2000-01-07

Publisher

Springer

Studio

Springer

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