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The purpose of this paper is to analyze numerically the blowup in finite time of the solutions to a one-dimensional, bidirectional, nonlinear wave model equation for the propagation of small-amplitude waves in shallow water, as a function of the relaxation time, linear and nonlinear drift, power of the nonlinear advection flux, viscosity coefficient, viscous attenuation, and amplitude, smoothness and width of three types of initial conditions.

An implicit, first-order accurate in time, finite difference method valid for semipositive relaxation times has been used to solve the equation in a truncated domain for three different initial conditions, a first-order time derivative initially equal to zero and several constant wave speeds.

The numerical experiments show a very rapid transient from the initial conditions to the formation of a leading propagating wave, whose duration depends strongly on the shape, amplitude and width of the initial data as well as on the coefficients of the bidirectional equation. The blowup times for the triangular conditions have been found to be larger than those for the Gaussian ones, and the latter are larger than those for rectangular conditions, thus indicating that the blowup time decreases as the smoothness of the initial conditions decreases. The blowup time has also been found to decrease as the relaxation time, degree of nonlinearity, linear drift coefficient and amplitude of the initial conditions are increased, and as the width of the initial condition is decreased, but it increases as the viscosity coefficient is increased. No blowup has been observed for relaxation times smaller than one-hundredth, viscosity coefficients larger than ten-thousandths, quadratic and cubic nonlinearities, and initial Gaussian, triangular and rectangular conditions of unity amplitude.

The blowup of a one-dimensional, bidirectional equation that is a model for the propagation of waves in shallow water, longitudinal displacement in homogeneous viscoelastic bars, nerve conduction, nonlinear acoustics and heat transfer in very small devices and/or at very high transfer rates has been determined numerically as a function of the linear and nonlinear drift coefficients, power of the nonlinear drift, viscosity coefficient, viscous attenuation, and amplitude, smoothness and width of the initial conditions for nonzero relaxation times.

This study aims to examine the role that four distinct bundles (developmental, utilisation, maintenance and accommodative) of HRM practices play in enhancing work engagement among chronically ill employees, and to analyse whether perceptions of discrimination on the grounds of illness can affect these relationships.

The data were collected through a quantitative survey using a sample of 669 chronically ill employees of a major Italian company.

This study's findings confirm the importance of discerning between positive, insignificant and negative effects of distinct HR bundles on chronically ill employees' work engagement. Furthermore, this study's results suggest that the positive effect of utilisation practices (i.e. practices aimed at enabling employees to make full use of existing, but not yet necessarily utilised, individual resources) on engagement is greater when chronically ill employees perceive a discrimination-free work environment.

This study's findings confirm the importance of discerning between positive, no, and negative effects of distinct HR bundles on chronically ill employees' work engagement. Furthermore, this study's results suggest that the positive effect of utilisation practices (i.e. practices aimed at enabling employees to make full use of existing but not necessarily applied individual resources) on engagement is greater when chronically ill employees perceive a discrimination-free work environment.

The study highlights those HR bundles that have the capacity to positively affect the work engagement of chronically ill employees, a minority group rarely considered in HRM studies. Furthermore, the research identifies perceived discrimination on the grounds of illness as a contextual condition that may hinder the otherwise positive effect of HRM practices on the engagement of workers suffering from a chronic illness.