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Qualitative and Quantitative Analysis of Nonlinear Systems [electronic resource] : Theory and Applications / by Michael Z. Zgurovsky, Pavlo O. Kasyanov.

By: Zgurovsky, Michael Z [author.].
Contributor(s): Kasyanov, Pavlo O [author.] | SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Studies in Systems, Decision and Control: 111Publisher: Cham : Springer International Publishing : Imprint: Springer, 2018Edition: 1st ed. 2018.Description: XXXIII, 240 p. 43 illus., 23 illus. in color. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783319598406.Subject(s): Computational intelligence | Dynamics | Nonlinear theories | Nonlinear Optics | Control engineering | Computational Intelligence | Applied Dynamical Systems | Nonlinear Optics | Control and Systems TheoryAdditional physical formats: Printed edition:: No title; Printed edition:: No title; Printed edition:: No titleDDC classification: 006.3 Online resources: Click here to access online
Contents:
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.
In: Springer Nature eBookSummary: 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.
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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.

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.

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