E-Book Overview
Discovering Evolution Equations with Applications: Volume 1-Deterministic Equations provides an engaging, accessible account of core theoretical results of evolution equations in a way that gradually builds intuition and culminates in exploring active research. It gives nonspecialists, even those with minimal prior exposure to analysis, the foundation to understand what evolution equations are and how to work with them in various areas of practice. After presenting the essentials of analysis, the book discusses homogenous finite-dimensional ordinary differential equations. Subsequent chapters then focus on linear homogenous abstract, nonhomogenous linear, semi-linear, functional, Sobolev-type, neutral, delay, and nonlinear evolution equations. The final two chapters explore research topics, including nonlocal evolution equations. For each class of equations, the author develops a core of theoretical results concerning the existence and uniqueness of solutions under various growth and compactness assumptions, continuous dependence upon initial data and parameters, convergence results regarding the initial data, and elementary stability results. By taking an applications-oriented approach, this self-contained, conversational-style book motivates readers to fully grasp the mathematical details of studying evolution equations. It prepares newcomers to successfully navigate further research in the field.
E-Book Content
Discovering Evolution Equations with Applications Volume 1-Deterministic Equations C9207_FM.indd 1 6/22/10 1:15:00 PM CHAPMAN & HALL/CRC APPLIED MATHEMATICS AND NONLINEAR SCIENCE SERIES Series Editors Goong Chen and Thomas J. Bridges Published Titles Advanced Differential Quadrature Methods, Zhi Zong and Yingyan Zhang Computing with hp-ADAPTIVE FINITE ELEMENTS, Volume 1, One and Two Dimensional Elliptic and Maxwell Problems, Leszek Demkowicz Computing with hp-ADAPTIVE FINITE ELEMENTS, Volume 2, Frontiers: Three Dimensional Elliptic and Maxwell Problems with Applications, Leszek Demkowicz, Jason Kurtz, David Pardo, Maciej Paszy´nski, Waldemar Rachowicz, and Adam Zdunek CRC Standard Curves and Surfaces with Mathematica®: Second Edition, David H. von Seggern Discovering Evolution Equations with Applications: Volume 1-Deterministic Equations, Mark A. McKibben Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics, Victor A. Galaktionov and Sergey R. Svirshchevskii Geometric Sturmian Theory of Nonlinear Parabolic Equations and Applications, Victor A. Galaktionov Introduction to Fuzzy Systems, Guanrong Chen and Trung Tat Pham Introduction to non-Kerr Law Optical Solitons, Anjan Biswas and Swapan Konar Introduction to Partial Differential Equations with MATLAB®, Matthew P. Coleman Introduction to Quantum Control and Dynamics, Domenico D’Alessandro Mathematical Methods in Physics and Engineering with Mathematica, Ferdinand F. Cap Mathematical Theory of Quantum Computation, Goong Chen and Zijian Diao Mathematics of Quantum Computation and Quantum Technology, Goong Chen, Louis Kauffman, and Samuel J. Lomonaco Mixed Boundary Value Problems, Dean G. Duffy Multi-Resolution Methods for Modeling and Control of Dynamical Systems, Puneet Singla and John L. Junkins Optimal Estimation of Dynamic Systems, John L. Crassidis and John L. Junkins Quantum Computing Devices: Principles, Designs, and Analysis, Goong Chen, David A. Church, Berthold-Georg Englert, Carsten Henkel, Bernd Rohwedder, Marlan O. Scully, and M. Suhail Zubairy A Shock-Fitting Primer, Manuel D. Salas Stochastic Partial Differential Equations, Pao-Liu Chow C9207_FM.indd 2 6/22/10 1:15:01 PM CHAPMAN & HALL/CRC APPLIED MATHEMATICS AND NONLINEAR SCIENCE SERIES Discovering Evolution Equations with Applications Volume 1-Deterministic Equations Mark