Theory and Applications of Abstract Semilinear Cauchy Problems

Pierre Magal, Shigui Ruan (Autoren)

Buch | Hardcover

XXII, 543 Seiten

2018 | 1st ed. 2018
Springer International Publishing (Verlag)
978-3-030-01505-3 (ISBN)

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Several types of differential equations, such as functional differential equation, age-structured models, transport equations, reaction-diffusion equations, and partial differential equations with delay, can be formulated as abstract Cauchy problems with non-dense domain. This monograph provides a self-contained and comprehensive presentation of the fundamental theory of non-densely defined semilinear Cauchy problems and their applications. Starting from the classical Hille-Yosida theorem, semigroup method, and spectral theory, this monograph introduces the abstract Cauchy problems with non-dense domain, integrated semigroups, the existence of integrated solutions, positivity of solutions, Lipschitz perturbation, differentiability of solutions with respect to the state variable, and time differentiability of solutions. Combining the functional analysis method and bifurcation approach in dynamical systems, then the nonlinear dynamics such as the stability of equilibria, center manifoldtheory, Hopf bifurcation, and normal form theory are established for abstract Cauchy problems with non-dense domain. Finally applications to functional differential equations, age-structured models, and parabolic equations are presented. This monograph will be very valuable for graduate students and researchers in the fields of abstract Cauchy problems, infinite dimensional dynamical systems, and their applications in biological, chemical, medical, and physical problems.

Dr. Pierre Magal is a professor in the Institut de Mathématiques de Bordeaux at the University of Bordeaux, France. His research interests are Differential Equations, Dynamical Systems, and Mathematical Biology. He studies nonlinear dynamics of abstract semilinear equations, functional differential equations, age-structured models, and parabolic systems. He is also interested in modeling some biological, epidemiological, and medical problems and studying the nonlinear dynamics of these models. Shigui Ruan is a professor in the Department of Mathematics at the University of Miami, Coral Gables, Florida, USA. His research interests are Differential Equations, Dynamical Systems, and Mathematical Biology. He studies nonlinear dynamics of some types of differential equations, such as the center manifold theory and Hopf bifurcation in semilinear evolution equations, multiple-parameter bifurcations in delay equations, and traveling waves in nonlocal reaction-diffusion systems. He is also interested in modeling and studying transmission dynamics of some infectious diseases (malaria, Rift Valley Fever, Hepatitis B virus, schistosomiasis, human rabies, SARS, West Nile virus, etc.) and nonlinear population dynamics.

Chapter 1- Introduction.- Chapter 2- Semigroups and Hille-Yosida Theorem.- Chapter 3- Integrated Semigroups and Cauchy Problems with Non-dense Domain.- Chapter 4- Spectral Theory for Linear Operators.- Chapter 5- Semilinear Cauchy Problems with Non-dense Domain.- Chapter 6- Center Manifolds, Hopf Bifurcation and Normal Forms.- Chapter 7- Functional Differential Equations.- Chapter 8- Age-structured Models.- Chapter 9- Parabolic Equations.- References.- Index.

"This interesting monograph can be a useful tool for researchers interested in the theory of abstract differential equations along with their applications, especially in age-structured models. However, it can be also used by graduate students as well as PhD students who are willing to get familiar with this theory. ... Remarks and Notes appearing at the end of each chapter are a good hint for further reading. The monograph is worth to be recommended." (Dariusz Bugajewski, zbMATH 1447.34002, 2020)
"This book will be of great interest for researchers studying abstract ODEs and their applications, especially for those with interest in nonlinear population dynamics, particularly in age-structured models." (Paul Georgescu, Mathematical Reviews, August, 2019)

Erscheinungsdatum	05.12.2018
Reihe/Serie	Applied Mathematical Sciences
Zusatzinfo	XXII, 543 p. 17 illus., 10 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	1009 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Schlagworte	abstract semilinear cauchy problems • age-structured models • Center manifold theory • densely and non-densely defined cauchy problems • Functional differential equations • Hopf Bifurcation • integrated semigroup theory • normal form theory • Ordinary differential equations • Parabolic equations • Partial differential equations • spectral theory of linear operators
ISBN-10	3-030-01505-X / 303001505X
ISBN-13	978-3-030-01505-3 / 9783030015053
Zustand	Neuware