Ti-Jun Xiao, Jin Liang

The Cauchy Problem for Higher Order Abstract Differential Equations (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 300
• Erscheinungstermin: 11. Dezember 2013
• Englisch
• ISBN-13: 9783540494799
• Artikelnr.: 53156303

Autorenporträt

Liang Jin received a BS and MSc in electrical engineering from the Changsha Institute of Technology, China, and a PhD in electrical engineering from the Chinese Academy of Space Technology. He is a senior member of the technical staff at Agere Systems in Allentown, Pennsylvania.

Inhaltsangabe

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.- Appendices: A1 Fractional powers of non-negative operators.- A2 Strongly continuous semigroups and cosine functions.- Bibliography.- Index.- Symbols.