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Qualitative and Quantitative Analysis of Nonlinear Systems

Part of the Studies in Systems, Decision and Control Book Series (volume 111)

DOI: 10.1007/978-3-319-59840-6

ISBN: 978-3-319-59839-0

Publisher: Springer International Publishing - Springer Journals

Jul 12, 2017

1 - 9 of 9 Chapters

LitStream

Qualitative Methods for Classes of Nonlinear Systems: Constructive Existence Results

Zgurovsky, Michael Z.; Kasyanov, Pavlo O.

Pages: 3 –45

[In this chapter we establish the existence results for classes of nonlinear systems. Section 2.1 devoted to the first order differential-operator equations and inclusions. In Sect. 2.2 we consider the second order operator differential equations and inclusions in special classes of...
LitStream

Regularity of Solutions for Nonlinear Systems

Zgurovsky, Michael Z.; Kasyanov, Pavlo O.

Pages: 47 –68

[In this chapter we establish sufficient conditions for regularity of all weak solutions for nonlinear systems. We note that the respective Cauchy problems may have nonunique weak solution. In Sect. 2.1 we establish regularity of all weak solutions for parabolic feedback control problems. Section...
LitStream

Advances in the 3D Navier-Stokes Equations

Zgurovsky, Michael Z.; Kasyanov, Pavlo O.

Pages: 69 –86

[In this chapter we provide a criterion for the existence of global strong solutions for the 3D Navier-Stokes system for any regular initial data. Moreover, we establish sufficient conditions for Leray-Hopf property of a weak solution for the 3D Navier-Stokes system. Under such conditions this...
LitStream

Strongest Convergence Results for Weak Solutions of Non-autonomous Reaction-Diffusion Equations with Carathéodory’s Nonlinearity

Zgurovsky, Michael Z.; Kasyanov, Pavlo O.

Pages: 89 –109

[In this chapter we consider the problem of uniform convergence results for all globally defined weak solutions of non-autonomous reaction-diffusionDifferential-operator equationreaction-diffusion system with Carathéodory’s nonlinearity satisfying standard sign and polynomial growth assumptions....
LitStream

Strongest Convergence Results for Weak Solutions of Feedback Control Problems

Zgurovsky, Michael Z.; Kasyanov, Pavlo O.

Pages: 111 –124

[In this chapter we establish strongest convergence results for weak solutions of feedback control problems. In Sect. 5.1 we set the problem. Section 5.2 devoted to the regularity of all weak solutions and their additional properties. In Sect. 5.3 we consider convergence of weak solutions results...
LitStream

Strongest Convergence Results for Weak Solutions of Differential-Operator Equations and Inclusions

Zgurovsky, Michael Z.; Kasyanov, Pavlo O.

Pages: 125 –158

[In this chapter we establish strongest convergence results for weak solutions of differential-operator equations and inclusions. In Sect. 6.1 we consider first order differential-operator equationsDifferential-operator equationfirst order and inclusionsDifferential-operator inclusionfirst order....
LitStream

Uniform Global Attractors for Non-autonomous Dissipative Dynamical Systems

Zgurovsky, Michael Z.; Kasyanov, Pavlo O.

Pages: 161 –177

[In this chapter we consider sufficient conditions for the existence of uniform compact global attractor for non-autonomous dynamical systems in special classes of infinite-dimensional phase spaces. The obtained generalizations allow us to avoid the restrictive compactness assumptions on the...
LitStream

Uniform Trajectory Attractors for Non-autonomous Nonlinear Systems

Zgurovsky, Michael Z.; Kasyanov, Pavlo O.

Pages: 179 –210

[In this chapter we study uniform trajectory attractors for non-autonomous nonlinear systems. In Sect. 8.1 we establish the existence of uniform trajectory attractor for non-autonomous reaction-diffusion equations with Carathéodory’s nonlinearity. Section 8.2 devoted to structural properties of...
LitStream

Indirect Lyapunov Method for Autonomous Dynamical Systems

Zgurovsky, Michael Z.; Kasyanov, Pavlo O.

Pages: 211 –237

[In this chapter we establish indirect Lyapunov methodIndirect Lyapunov method for autonomous dynamical systems. Section 9.1 devoted to the first order autonomous differential-operator equations and inclusions. In Sect. 9.2 we consider the second order autonomous operator differential equations...

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