Asymptotic Behavior of Solutions for the Cauchy Problem of a Dissipative Boussinesq-Type Equation

We consider the Cauchy problem for an evolution equation modeling bidirectional surface waves in a convecting fluid. Under small condition on the initial value, the existence and asymptotic behavior of global solutions in some time weighted spaces are established by the contraction mapping principle

Sharp well-posedness of the Ostrovsky, Stepanyams and Tsimring equation

In this paper, we study the Ostrovsky, Stepanyams and Tsimring equation. We show that the associated initial value problem is locally well-posed in Sobolev spaces $H^sleft(mathbb{R}right)$ for $s>-3/2$. We also prove that our result is sharp in the sense that the flow map of this equation fails to be $C^2$ in $H^s(mathbb{R})$ for $s<-3/2$

A Nutty Approach to Disease Prevention

Tree nuts are healthy foods with a favourable macro- and micronutrient profile. They are low in sat-urated fats and high in mono- and polyunsaturated fatty acids. They are also good sources of vegeta-ble protein, fiber, phytosterols, polyphenols, vitamins and minerals. Because of this healthy nutrient profile, it has been postulated that tree nuts may play a significant role in health maintenance and disease prevention. The purpose of this paper is 1) to provide a brief overview of the current scien-tific evidence on the role of tree nuts in prevention and management of diabetes and heart disease and 2) to outline some of the key challenges for recommending nuts as part of a healthy diet to pa-tients with or at risk of diabetes or heart disease

Angular traveling waves of the high-dimensional Boussinesq equation

This paper studies traveling waves with nonzero wave speed (angular traveling waves) of the high-dimensional Boussinesq equation that have not been studied before. We analyze the properties of these waves and demonstrate that, unlike the unique stationary solution, they lack positivity, radial symmetry, and exponential decay. By employing variational and geometric approaches, along with perturbation theory, we establish the orbital (in)stability and strong instability of these traveling waves.Comment: Comments welcom

A robust AHP-DEA method for measuring the relative efficiency: An application of airport industry

Measuring the relative efficiency of similar units has been an important topic of research among many researchers. Data envelopment analysis has been one of the most important techniques for measuring the efficiency of different units. However, there are some limitations on using such technique and some people prefer to use other methods such as analytical hierarchy process to measure the relative efficiencies. Besides, uncertainty in the input data is another issue, which makes some misleading results. In this paper, we present an integrated robust DEA-AHP to measure the relative efficiency of similar units. The proposed model of this is believed to capable of presenting better results in terms of efficiency compared with exclusive usage of DEA or AHP. The implementation of the proposed model is demonstrated for a real-world case study of Airport industry and the results are analyzed

Long time behavior of solutions to the generalized Boussinesq equation in Sobolev spaces

In this paper, we study the generalized Boussinesq equation to model the water wave problem with surface tension. First, we investigate the initial value problem in the Sobolev spaces. We derive some conditions under which the solutions of this equation are global or blow-up in time, and next, we extend our results to the Bessel potential spaces. The asymptotic behavior of the solutions is also determined. The non-existence of solitary waves for some parameters is proved using Pohozaev-type identities. We generate solitary wave solutions of generalized Boussinesq equation using the Petviashvili iteration method numerically. In order to investigate the time evolution of solutions to the generalized Boussinesq equation, we propose the Fourier pseudo-spectral numerical method. After studying the time evolution of the single solitary wave, we focus on the gap interval where neither a global existence nor a blow-up result has been established theoretically. Our numerical results successfully fill the gaps left by the theoretical ones