Semilinear Evolution Equations And Their Applications

This book, which is a continuation of Almost Automorphic Type and Almost Periodic Type Functions in Abstract Spaces, presents recent trends and developments upon fractional, first, and second order semilinear difference and differential equations, including degenerate ones. Various stability, uniqueness, and existence results are established using various tools from nonlinear functional analysis and operator theory (such as semigroup methods). Various applications to partial differential equations and the dynamic of populations are amply discussed. This self-contained volume is primarily intended for advanced undergraduate and graduate students, post-graduates and researchers, but may also be of interest to non-mathematicians such as physicists and theoretically oriented engineers. It can also be used as a graduate text on evolution equations and difference equations and their applications to partial differential equations and practical problems arising in population dynamics. For completeness, detailed preliminary background on Banach and Hilbert spaces, operator theory, semigroups of operators, and almost periodic functions and their spectral theory are included as well.

This book presents in a self-contained form the typical basic properties of solutions to semilinear evolutionary partial differential equations, with special emphasis on global properties. It has a didactic ambition and will be useful for an applied readership as well as theoretical researchers.

This monograph is intended to present the fundamentals of the theory of abstract parabolic evolution equations and to show how to apply to various nonlinear dif- sion equations and systems arising in science. The theory gives us a uni?ed and s- tematic treatment for concrete nonlinear diffusion models. Three main approaches are known to the abstract parabolic evolution equations, namely, the semigroup methods, the variational methods, and the methods of using operational equations. In order to keep the volume of the monograph in reasonable length, we will focus on the semigroup methods. For other two approaches, see the related references in Bibliography. The semigroup methods, which go back to the invention of the analytic se- groups in the middle of the last century, are characterized by precise formulas representing the solutions of the Cauchy problem for evolution equations. The ?tA analytic semigroup e generated by a linear operator ?A provides directly a fundamental solution to the Cauchy problem for an autonomous linear e- dU lution equation, +AU =F(t), 0

Annotation Ito (North Carolina State U.) and Kappel (U. of Graz, Austria) offer a unified presentation of the general approach for well-posedness results using abstract evolution equations, drawing from and modifying the work of K. and Y. Kobayashi and S. Oharu. They also explore abstract approximation results for evolution equations. Their work is not a textbook, but they explain how instructors can use various sections, or combinations of them, as a foundation for a range of courses. Annotation copyrighted by Book News, Inc., Portland, OR

Part of the Pitman Research Notes in Mathematics series, this text covers: linear evolution equations of parabolic type; semilinear evolution equations of parabolic type; evolution equations and positivity; semilinear periodic evolution equations; and applications.

The international conference on which the book is based brought together many of the world's leading experts, with particular effort on the interaction between established scientists and emerging young promising researchers, as well as on the interaction of pure and applied mathematics. All material has been rigorously refereed. The contributions contain much material developed after the conference, continuing research and incorporating additional new results and improvements. In addition, some up-to-date surveys are included.

This volume presents a collection of lectures on linear partial differntial equations and semigroups, nonlinear equations, stochastic evolutionary processes, and evolution problems from physics, engineering and mathematical biology. The contributions come from the 6th International Conference on Evolution Equations and Their Applications in Physica