The Cauchy Problem for Higher Order Abstract Differential Equations (Lecture Notes in Mathematics, 1701, Band 1701) - Softcover

Liang, Jin; Xiao, Ti-Jun

Softcover

ISBN 10: 3540652388 ISBN 13: 9783540652380

Verlag: Springer, 2008

Inhaltsangabe

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.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 2008
• Sprache: Englisch
• ISBN 10: 3540652388
• ISBN 13: 9783540652380
• Einband: Taschenbuch
• Anzahl der Seiten: 324
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