Theory and Applications of Abstract Semilinear Cauchy 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)