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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.
This book constitutes the proceedings of the 11th International Conference on Artificial Intelligence and Mobile Services, AIMS 2022, held as Part of the Services Conference Federation, SCF 2022, held in Honolulu, HI, USA, in December 2022. The 10 full papers presented in this volume were carefully reviewed and selected from 22 submissions. The International Conference on AI & Mobile Services (AIMS 2022) aims at providing an international forum that is dedicated to exploring different aspects of AI (from technologies to approaches and algorithms) and mobile services (from business management to computing systems, algorithms, and applications) to promoting technological innovations in research and development of mobile services, including, but not limited to, wireless & sensor networks, mobile & wearable computing, mobile enterprise & eCommerce, ubiquitous collaborative & social services, machine-to-machine & Internet-of-things clouds, cyber-physical integration, and big data analytics for mobility-enabled services.
This volume of Advances in Evolution Equations is dedicated to the memory of Professor Vasilii Vasilievich Zhikov, an outstanding Russian mathematician. Zhikov's scientific interest ranged from almost periodic differential equations and topological dynamics to spectral theory of elliptic operators, qualitative theory of parabolic equations, calculus of variations, homogenization, and hydrodynamics, to name a few. Many of his results are now classical.
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