Blow-up and global existence for a general class of nonlocal nonlinear coupled wave equations

We study the initial-value problem for a general class of nonlinear nonlocal coupled wave equations. The problem involves convolution operators with kernel functions whose Fourier transforms are nonnegative. Some well-known examples of nonlinear wave equations, such as coupled Boussinesq-type equations arising in elasticity and in quasi-continuum approximation of dense lattices, follow from the present model for suitable choices of the kernel functions. We establish local existence and sufficient conditions for finite time blow-up and as well as global existence of solutions of the problem.Comment: 11 pages. Minor changes and added reference

The Camassa-Holm equation as the long-wave limit of the improved Boussinesq equation and of a class of nonlocal wave equations

In the present study we prove rigorously that in the long-wave limit, the unidirectional solutions of a class of nonlocal wave equations to which the improved Boussinesq equation belongs are well approximated by the solutions of the Camassa-Holm equation over a long time scale. This general class of nonlocal wave equations model bidirectional wave propagation in a nonlocally and nonlinearly elastic medium whose constitutive equation is given by a convolution integral. To justify the Camassa-Holm approximation we show that approximation errors remain small over a long time interval. To be more precise, we obtain error estimates in terms of two independent, small, positive parameters $\epsilon$ and $\delta$ measuring the effect of nonlinearity and dispersion, respectively. We further show that similar conclusions are also valid for the lower order approximations: the Benjamin-Bona-Mahony approximation and the Korteweg-de Vries approximation.Comment: 24 pages, to appear in Discrete and Continuous Dynamical System

The Cauchy problem for a class of two-dimensional nonlocal nonlinear wave equations governing anti-plane shear motions in elastic materials

This paper is concerned with the analysis of the Cauchy problem of a general class of two-dimensional nonlinear nonlocal wave equations governing anti-plane shear motions in nonlocal elasticity. The nonlocal nature of the problem is reflected by a convolution integral in the space variables. The Fourier transform of the convolution kernel is nonnegative and satisfies a certain growth condition at infinity. For initial data in $L^{2}$ Sobolev spaces, conditions for global existence or finite time blow-up of the solutions of the Cauchy problem are established.Comment: 15 pages. "Section 6 The Anisotropic Case" added and minor changes. Accepted for publication in Nonlinearit

The Camassa-Holm equation as the long-wave limit of the improved Boussinesq equation and of a class of nonlocal wave equations

In the present study we prove rigorously that in the long-wave limit, the unidirectional solutions of a class of nonlocal wave equations to which the improved Boussinesq equation belongs are well approximated by the solutions of the Camassa-Holm equation over a long time scale. This general class of nonlocal wave equations model bidirectional wave propagation in a nonlocally and nonlinearly elastic medium whose constitutive equation is given by a convolution integral. To justify the Camassa-Holm approximation we show that approximation errors remain small over a long time interval. To be more precise, we obtain error estimates in terms of two independent, small, positive parameters is an element of and delta measuring the effect of nonlinearity and dispersion, respectively. We further show that similar conclusions are also valid for the lower order approximations: the Benjamin-Bona-Mahony approximation and the Korteweg-de Vries approximation

The Null Effect of Chewing Gum during Hemodialysis on Dry Mouth

PubMed ID: 27509571Aims and Objectives: The study was conducted to determine the effect of chewing gum during hemodialysis on dry mouth and its symptoms. Background: The imposition of fluid restriction and the use of medications that reduce saliva production may lead to dry mouth. Design: This study is a randomized, controlled, single-blind, crossover experimental study. Methods: The subjects consisted of 61 hemodialysis patients recruited from 4 dialysis centers in southern Turkey. The data were collected using a Patient Identification Form, a Form for Assessing the Symptoms of Dry Mouth, and a Patient Follow-up Form. Saliva samples were obtained for analysis of flow rates. Results: The salivary flow rates of the patients increased during the first hour on the day when gum was chewed, and this increase was statistically significant. However, no significant difference was found between the salivary flow rates at the 0- and 4-hour time points on the day when gum was chewed (P >.05). In addition, the salivary pH values were in the normal range on both days, although the pH values tended to be more acidic on the day when gum was not chewed. Conclusions: Overall, it was found that chewing gum for 15 minutes each hour during a hemodialysis session did not increase the saliva amount, maintain the pH value of the saliva within a normal range, or control dry mouth symptoms. Copyright © 2016 Wolters Kluwer Health, Inc. All rights reserved

factors causing interruptions

Aim This study was conducted in an attempt to examine the number and duration of interruptions during the medication preparation process and to identify the factors causing these interruptions.Background Interruptions during the medication preparation process can cause medication errors owing to nurses' lack of attention.Method A descriptive study was conducted at the Internal Diseases and General Surgery services of a university hospital between 15 June 2012 and 30 July 2012. The data were collected using the 'Observation Form of Preparing Medication.'Result A total of 122 observations were made in the study. It was found that there was an interruption during the process of preparing medication in 95.9% of observations. The average number (+/- SD) of interruptions was 5.8 +/- 4. The individuals causing the interruption during medication preparation were primarily nurses working in the same service. Receiving from or giving materials to the treatment room were the main reasons for the interruptions.Conclusion This study found a very high interruption rate during the process of preparing medications

Interruption of the medication preparation process and an examination of factors causing interruptions.

AIM: This study was conducted in an attempt to examine the number and duration of interruptions during the medication preparation process and to identify the factors causing these interruptions. BACKGROUND: Interruptions during the medication preparation process can cause medication errors owing to nurses' lack of attention. METHOD: A descriptive study was conducted at the Internal Diseases and General Surgery services of a university hospital between 15 June 2012 and 30 July 2012. The data were collected using the 'Observation Form of Preparing Medication.' RESULT: A total of 122 observations were made in the study. It was found that there was an interruption during the process of preparing medication in 95.9% of observations. The average number (±SD) of interruptions was 5.8 ± 4. The individuals causing the interruption during medication preparation were primarily nurses working in the same service. Receiving from or giving materials to the treatment room were the main reasons for the interruptions. CONCLUSION: This study found a very high interruption rate during the process of preparing medications. IMPLICATIONS FOR NURSING MANAGEMENT: As interruptions during medication preparation can cause medical errors, in-service teaching should be provided to raise awareness for this important issue. The findings of the study can be useful for enhancing the conditions of the physical environment, separating the treatment rooms and using the treatment rooms only for preparing medication