Título: Abstract Volterra Integro-Differential Equations
Autor: Marko Kostic
Sinopse: The theory of linear Volterra integro-differential equations has been developing rapidly in the last three decades. This book provides an easy to read concise introduction to the theory of ill-posed abstract Volterra integro-differential equations. A major part of the research is devoted to the study of various types of abstract (multi-term) fractional differential equations with Caputo fractional derivatives, primarily from their invaluable importance in modeling of various phenomena appearing in physics, chemistry, engineering, biology and many other sciences. The book also contributes to the theories of abstract first and second order differential equations, as well as to the theories of higher order abstract differential equations and incomplete abstract Cauchy problems, which can be viewed as parts of the theory of abstract Volterra integro-differential equations only in its broad sense. The operators examined in our analyses need not be densely defined and may have empty resolvent set. Divided into three chapters, the book is a logical continuation of some previously published monographs in the field of ill-posed abstract Cauchy problems. It is not written as a traditional text, but rather as a guidebook suitable as an introduction for advanced graduate students in mathematics or engineering science, researchers in abstract partial differential equations and experts from other areas. Most of the subject matter is intended to be accessible to readers whose backgrounds include functions of one complex variable, integration theory and the basic theory of locally convex spaces. An important feature of this book as compared to other monographs and papers on abstract Volterra integro-differential equations is, undoubtedly, the consideration of solutions, and their hypercyclic properties, in locally convex spaces. Each chapter is further divided in sections and subsections and, with the exception of the introductory one, contains a plenty of examples and open problems. The numbering of theorems, propositions, lemmas, corollaries, and definitions are by chapter and section. The bibliography is provided alphabetically by author name and a reference to an item is of the form, The book does not claim to be exhaustive. Degenerate Volterra equations, the solvability and asymptotic behaviour of Volterra equations on the line, almost periodic and positive solutions of Volterra equations, semilinear and quasilinear problems, as some of many topics are not covered in the book. The authors justification for this is that it is not feasible to encompass all aspects of the theory of abstract Volterra equations in a single monograph.
Contexto da obra
Quando a classificação é mais ampla, o contexto do livro costuma depender ainda mais de autoria, tema e edição. “Abstract Volterra Integro-Differential Equations”, de Marko Kostic, publicado pela editora CRC Press, em 2015 e com 484 páginas, integra a categoria Livros Variados. Por isso, autoria, edição e tema acabam tendo ainda mais peso na forma de apresentar o livro.
Editora: CRC Press
Páginas: 484
Ano: 2015
Edição:
Linguagem: English
ISBN: 148225431X
ISBN13: 9781482254310
Sobre a editora
Os livros da editora CRC Press apresentam uma leitura densa e focada em áreas técnicas e científicas, com ênfase em temas como ciências da vida, engenharia, matemática aplicada e ciências da computação. A experiência de leitura tende a ser informativa e detalhada, com textos que combinam rigor teórico e aplicações práticas, muitas vezes voltados para profissionais, pesquisadores e estudantes avançados. O tom é predominantemente formal e didático, privilegiando a clareza na exposição de conceitos complexos e dados técnicos. O catálogo revela uma predominância de obras que abordam desde fundamentos até avanços recentes, com formatos que incluem guias práticos, compêndios e referências especializadas. Há obras que exploram tanto aspectos teóricos, como modelagem matemática e física, quanto aplicações em áreas como medicina, toxicologia, segurança digital e engenharia de alimentos.
