Overview
- Authors:
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Ti-Jun Xiao
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Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, People’s Republic of China
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Jin Liang
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Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, People’s Republic of China
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Table of contents (7 chapters)
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Front Matter
Pages N2-XII
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Back Matter
Pages 263-309
About this book
The main purpose of this book is to present the basic theory and some recent de 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 trans 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.
Authors and Affiliations
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Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, People’s Republic of China
Ti-Jun Xiao,
Jin Liang
