Blow-up and energy decay for a class of wave equations with nonlocal Kirchhoff-type diffusion and weak damping

The purpose of this paper is to study the following equation driven by a nonlocal integro-differential operator $\mathcal{L}_K$: \[u_{tt}+[u]_s^{2(\theta-1)}\mathcal{L}_Ku+a|u_t|^{m-1}u_t=b|u|^{p-1}u\] with homogeneous Dirichlet boundary condition and initial data, where $[u]^2_s$ is the Gagliardo seminorm, $a\geq 0,~b>0,~0

Stabilization of inter-area oscillations in two-area test system via centralized interval type-2 fuzzy-based dynamic brake control

Inter-area oscillations are, by far, the most detrimental oscillation category to the integrity of synchronously interconnected power systems. Inter-area oscillations are characterized by the inherent weak damping. The inherent poor damping associated with the inter-area oscillations leaves open wide probabilities for irrevocable widespread blackouts with the consequent eventual devastating outcomes measured in terms of the huge economic casualties and the possible human fatalities. The main purpose of this work is to mitigate inter-area power oscillations. This article explores the effectiveness of dual thyristor controlled braking resistor units with Interval Type-2 fuzzy-based centralized architecture for neutralizing the jeopardy of inter-area power oscillations in Kundur’s two-area test system using MATLAB™/Simulink environment. The effectiveness of the proposed scheme is examined by considering four case studies with different degrees of severity. The simulation results show that the proposed scheme is simple yet effective in treating the inter-area oscillations appropriately under the considered case studies.

Long-time behavior for fourth-order wave equations with strain term and nonlinear weak damping term

<p style='text-indent:20px;'>We mainly focus on the asymptotic behavior analysis for certain fourth-order nonlinear wave equations with strain term, nonlinear weak damping term and source term. We establish two theorems on the asymptotic behavior of the solution depending on some conditions related to the relationship among the forced strain term, the nonlinear weak damping term and source terms.</p>

Global existence, asymptotic behavior and uniform attractor for a non-autonomous Timoshenko system of type III with weak damping

In this paper, we investigate one-dimensional thermoelastic system of Timoshenko type III with double memory dampings. At first we give the global existence of solutions by using semigroup theory. Then we can prove the energy decay of solutions by constructing a series of Lyapunov functionals and obtain the existence of absorbing ball. Finally, we prove the asymptotic compactness by using uniform contractive functions and obtain the existence of uniform attractor.

Ocean Applications

In this chapter, the most promising techniques to observe oil slicks and to detect metallic targets at sea using polarimetric synthetic aperture radar (SAR) data are reviewed and critically analysed. The detection of oil slicks in SAR data is made difficult not only by the presence of speckle but also by the presence of, e.g. biogenic films, low-wind areas, rain cells, currents, etc., which increase the false alarm probability. The use of polarimetric features has been shown to both observe oil slicks and distinguish them from weak-damping look-alikes but also to extract some of their properties. Similarly to oil slicks, the same factors can hamper the detection of metallic targets at sea. The radiometric information provided by traditional single-channel SAR is not generally sufficient to unambiguously detect man-made metallic targets over the sea surface. This shortcoming is overcome by employing polarimetry, which allows to fully characterize the scattering mechanism of such targets.