Qualitative and Quantitative Analysis of Nonlinear Systems

Here, the authors present modern methods of analysis for nonlinear systems which may occur in fields such as physics, chemistry, biology, or economics. They concentrate on the following topics, specific for such systems:

(a) constructive existence results and regularity theorems for all weak solutions;

(b) convergence results for solutions and their approximations;

(c) uniform global behavior of solutions in time; and

(d) pointwise behavior of solutions for autonomous problems with possible gaps by the phase variables. The general methodology for the investigation of dissipative dynamical systems with several applications including nonlinear parabolic equations of divergent form, nonlinear stochastic equations of parabolic type, unilateral problems, nonlinear PDEs on Riemannian manifolds with or without boundary, contact problems as well as particular examples is established. As such, the book is addressed to a wide circle of mathematical, mechanical and engineering readers.

Focuses on specific topics of nonlinear systems Includes constructive existence results and regularity theorems for all weak solutions Presents convergence results for solutions and their approximations in strongest topologies of the natural phase and extended phase spaces Explains uniform global behavior of solutions in time and pointwise behavior of solutions for autonomous problems with possible gaps by the phase variables Discusses numerous applications, including applied problems in physics, chemistry, biology and economics Is addressed to a wide readership from the fields of mathematics, mechanics and engineering Includes supplementary material: sn.pub/extras

Inhalt
Introduction: Special Classes of Extended Phase Spaces of Distributions.- Qualitative Methods for Classes of Nonlinear Systems: Constructive Existence Results.- Regularity of Solutions for Nonlinear Systems.- Uniform Global Attractors for Non-Autonomous Dissipative Dynamical Systems.- Uniform Trajectory Attractors for Non-autonomous Nonlinear Systems.- Indirect Lyapunov Method for Autonomous Dynamical Systems