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The Cauchy Problem for Higher Order Abstract Differential Equations : Lecture Notes in Mathematics - Ti-Jun Xiao

The Cauchy Problem for Higher Order Abstract Differential Equations

Lecture Notes in Mathematics

Paperback Published: 18th November 1998
ISBN: 9783540652380
Number Of Pages: 300

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The main purpose of this book is to present the basic theory and some recent deĀ­ velopments concerning the Cauchy problem for higher order abstract differential equations u(n)(t) + ~ AiU(i)(t) = 0, t ~ 0, { U(k)(O) = Uk, 0 ~ k ~ n-l. where AQ, Ab . . . , A - are linear operators in a topological vector space E. n 1 Many problems in nature can be modeled as (ACP ). For example, many n initial value or initial-boundary value problems for partial differential equations, stemmed from mechanics, physics, engineering, control theory, etc. , can be transĀ­ lated into this form by regarding the partial differential operators in the space variables as operators Ai (0 ~ i ~ n - 1) in some function space E and letting the boundary conditions (if any) be absorbed into the definition of the space E or of the domain of Ai (this idea of treating initial value or initial-boundary value problems was discovered independently by E. Hille and K. Yosida in the forties). The theory of (ACP ) is closely connected with many other branches of n mathematics. Therefore, the study of (ACPn) is important for both theoretical investigations and practical applications. Over the past half a century, (ACP ) has been studied extensively.

Laplace transforms and operator families in locally convex spaces
Wellposedness and solvability
Generalized wellposedness
Analyticity and parabolicity
Exponential growth bound and exponential stability
Differentiability and norm continuity
Almost periodicity
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9783540652380
ISBN-10: 3540652388
Series: Lecture Notes in Mathematics
Audience: General
Format: Paperback
Language: English
Number Of Pages: 300
Published: 18th November 1998
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.39 x 15.6  x 1.73
Weight (kg): 0.45