scholarly journals Strong Uniform Attractors for Nonautonomous Suspension Bridge-Type Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-19
Author(s):  
Xuan Wang ◽  
Qiaozhen Ma
Keyword(s):  
Hilbert Space ◽  
Dynamical Behavior ◽  
Type Equation ◽  
Strong Solutions ◽  
Suspension Bridge ◽  
Bridge Type ◽  
Uniform Attractors ◽  
External Forces ◽  
Higher Regularity

We discuss long-term dynamical behavior of the solutions for the nonautonomous suspension bridge-type equation in the strong Hilbert spaceD(A)×H2(Ω)∩H01(Ω), where the nonlinearityg(u,t)is translation compact and the time-dependent external forcesh(x,t)only satisfy condition (C*) instead of translation compact. The existence of strong solutions and strong uniform attractors is investigated using a new process scheme. Since the solutions of the nonautonomous suspension bridge-type equation have no higher regularity and the process associated with the solutions is not continuous in the strong Hilbert space, the results are new and appear to be optimal.

scholarly journals Random attractors for the stochastic coupled suspension bridge equations of Kirchhoff type

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Ling Xu ◽  
Jianhua Huang ◽  
Qiaozhen Ma
Keyword(s):  
Existence And Uniqueness ◽  
Dynamical Behavior ◽  
Suspension Bridge ◽  
Random Dynamical System ◽  
Random Set ◽  
Kirchhoff Type ◽  
Random Attractors ◽  
Long Term Behavior ◽  
Uniqueness Of A Solution

Abstract This paper is devoted to the dynamical behavior of stochastic coupled suspension bridge equations of Kirchhoff type. For the deterministic cases, there are many classical results such as existence and uniqueness of a solution and long-term behavior of solutions. To the best of our knowledge, the existence of random attractors for the stochastic coupled suspension bridge equations of Kirchhoff type is not yet considered. We intend to investigate these problems. We first obtain the dissipativeness of a solution in higher-energy spaces $H^{3}(U)\times H_{0}^{1}(U)\times (H^{2}(U)\cap H_{0}^{1}(U))\times H_{0}^{1}(U)$ H 3 ( U ) × H 0 1 ( U ) × ( H 2 ( U ) ∩ H 0 1 ( U ) ) × H 0 1 ( U ) . This implies that the random dynamical system generated by the equation has a random attractor in $(H^{2}(U)\cap H_{0}^{1}(U))\times L^{2}(U) \times H_{0}^{1}(U)\times L^{2}(U)$ ( H 2 ( U ) ∩ H 0 1 ( U ) ) × L 2 ( U ) × H 0 1 ( U ) × L 2 ( U ) , which is a tempered random set in the space in $H^{3}(U)\times H_{0}^{1}(U)\times (H^{2}(U)\cap H_{0} ^{1}(U))\times H_{0}^{1}(U)$ H 3 ( U ) × H 0 1 ( U ) × ( H 2 ( U ) ∩ H 0 1 ( U ) ) × H 0 1 ( U ) .

The Motion of Floating Systems: Nonlinear Dynamics in Periodic and Random Waves

2009 ◽  
Vol 131 (4) ◽  
Author(s):  
Katrin Ellermann
Keyword(s):  
Dynamical Behavior ◽  
Nonlinear Behavior ◽  
Operating Conditions ◽  
Random Waves ◽  
Multiple Components ◽  
Random Disturbances ◽  
Restoring Forces ◽  
Steady State Responses ◽  
External Forces ◽  
Floating Systems

Floating systems, such as ships, barges, or semisubmersibles, show a dynamical behavior, which is determined by their internal structure and the operating conditions caused by external forces e.g., due to waves and wind. Due to the complexity of the system, which commonly includes coupling of multiple components or nonlinear restoring forces, the response can exhibit inherently nonlinear characteristics. In this paper different models of floating systems are considered. For the idealized case of purely harmonic forcing they all show nonlinear behavior such as subharmonic motion or different steady-state responses at constant operating conditions. The introduction of random disturbances leads to deviations from the idealized case, which may change the overall response significantly. Advantages and limitations of the different mathematical models and the applied numerical techniques are discussed.

Physical–spatial–technological environments and successful ageing

2021 ◽  
pp. 43-50
Author(s):  
Clemens Tesch-Römer ◽  
Hans-Werner Wahl ◽  
Suresh I. S. Rattan ◽  
Liat Ayalon
Keyword(s):  
Point Of View ◽  
Successful Ageing ◽  
Term Care ◽  
Lack Of Fit ◽  
Person Environment Fit ◽  
Environment Agency ◽  
External Forces ◽  
Practical Implications ◽  
Practical Sense

In this chapter the authors argue that physical, spatial, and technological environments are relevant to successful ageing both in a conceptual and in a practical sense. Conceptually, efforts towards ageing successfully cannot be discussed separately from the various external forces that serve as constraining or enhancing influences in this respect. From a practical point of view, interventions aimed at improving one’s environment become increasingly relevant as an individual’s resources and reserve capacities dwindle. Environments for ageing successfully may be characterized in terms of person–environment docility vs proactivity, person–environment fit vs lack of fit, and person–environment agency vs belonging. The authors link these concepts with various models of successful ageing and discuss practical implications for housing, long-term care environments, neighbourhoods, municipalities, and use of digital technology.

scholarly journals Strong Solutions of the Incompressible Navier–Stokes–Voigt Model

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 181
Author(s):  
Evgenii S. Baranovskii
Keyword(s):  
Three Dimensional ◽  
Strong Solutions ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Navier Stokes ◽  
Evolutionary Equation ◽  
Long Time ◽  
Special Basis ◽  
External Forces ◽  
Initial Boundary Value

This paper deals with an initial-boundary value problem for the Navier–Stokes–Voigt equations describing unsteady flows of an incompressible non-Newtonian fluid. We give the strong formulation of this problem as a nonlinear evolutionary equation in Sobolev spaces. Using the Faedo–Galerkin method with a special basis of eigenfunctions of the Stokes operator, we construct a global-in-time strong solution, which is unique in both two-dimensional and three-dimensional domains. We also study the long-time asymptotic behavior of the velocity field under the assumption that the external forces field is conservative.

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