A shooting argument approach to a sharp type solution for nonlinear degenerate Fisher-KPP equations

In this paper we prove the existence and uniqueness of a travelling-wave solution of sharp type for the degenerate (at u = 0) parabolic equation $u_1 = [D(u)u_x]_x + g(u)$ where D is a strictly increasing function and g is a function which generalizes the kinetic part of the classical Fisher-KPP equation. The original problem is transformed into the proper travelling-wave variables, and then a shooting argument is used to show the existence of a saddle-saddle heteroclinic trajectory for a critical value, c*>0, of the speed c of an autonomous system of ordinary differential equations. Associated with this connection is a sharp-type solution of the nonlinear partial differential equation

A non-linear degenerate equation for direct aggregation and traveling wave dynamics

The gregarious behavior of individuals of populations is an important factor in avoiding predators or for reproduction. Here, by using a random biased walk approach, we build a model which, after a transformation, takes the general form [u_{t}=[D(u)u_{x}]_{x}+g(u)] . The model involves a density-dependent non-linear diffusion coefficient [D] whose sign changes as the population density [u] increases. For negative values of [D] aggregation occurs, while dispersion occurs for positive values of [D] . We deal with a family of degenerate negative diffusion equations with logistic-like growth rate [g] . We study the one-dimensional traveling wave dynamics for these equations and illustrate our results with a couple of examples. A discussion of the ill-posedness of the partial differential equation problem is included

Travelling waves in a nonlinear degenerate diffusion model for bacterial pattern formation

We study a reaction diffusion model recently proposed in [5] to describe the spatiotemporal evolution of the bacterium Bacillus subtilis on agar plates containing nutrient. An interesting mathematical feature of the model, which is a coupled pair of partial differential equations, is that the bacterial density satisfies a degenerate nonlinear diffusion equation. It was shown numerically that this model can exhibit quasi-one-dimensional constant speed travelling wave solutions. We present an analytic study of the existence and uniqueness problem for constant speed travelling wave solutions. We find that such solutions exist only for speeds greater than some threshold speed giving minimum speed waves which have a sharp profile. For speeds greater than this minimum speed the waves are smooth. We also characterise the dependence of the wave profile on the decay of the front of the initial perturbation in bacterial density. An investigation of the partial differential equation problem establishes,via a global existence and uniqueness argument, that these waves are the only long time solutions supported by the problem. Numerical solutions of the partial differential equation problem are presented and they confirm the results of the analysis

A review on travelling wave solutions of one-dimensional reaction diffusion equations with non-linear diffusion term

In this paper we review the existence of different types of travelling wave solutions $u(x,t) = \phi(x - ct)$ of degenerate non-linear reaction-diffusion equations of the form $u_t = [D(u)u_x]_x + g(u)$ for different density-dependent diffusion coefficients D and kinetic part g. These include the non-linear degenerate generalized Fisher-KPP and the Nagumo equations. Also, we consider an equation whose diffusion coefficient changes sign as the diffusive substance increases. This describes a diffusive-aggregative process. In this case the travelling wave solutions are explored and the ill-posedness of two boundary-value problems associated with the above equation is stated

Spatial dynamics in speciation

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Travelling waves in density-dependent dispersion models

Many models have been proposed to account for the spatial dispersion of population of insects, bacteria, etc. Some species migrate from densely populated areas into sparsely populated regions to avoid overcrowding, while other species have a tendency to aggregate

La importancia del Sistema de Gestión de Calidad en la Asociación Mutualista Ambato

El reto de lograr el crecimiento del sector financiero en toda América Latina incluyendo Ecuador demuestra la importancia y la necesidad del mismo en toda la región para lo cual es necesario mejorar el sector empezando por cada una de las instituciones y una manera de hacerlo es incrementando la calidad de los procesos y sus servicios mediante un SGC (Sistema de Gestión de Calidad).   Los SGC según la revisión en la literatura tienen cada vez más importancia en todo el mundo debido a su simplicidad para ser aplicados además que se pueden adaptar a todas las empresas, instituciones u organizaciones que requieran mejorar la calidad ya sea de su producción o del servicio que se preste. La finalidad de las   instituciones financieras es el brindar créditos para diversos fines como los de adquirir una vivienda entre otros apoyando de esa manera a la mejora de la calidad de vida de la ciudadaní­a. La investigación se enfocó en la mejora de la calidad de los procesos por medio de un SGC en donde los resultados indicaron que dicho sistema puede facilitar el control y el mejoramiento de sus procesos motivo por el cual es necesario la implementación mediante la norma ISO 9001:2015

Cost-effectiveness analysis for joint pain treatment in patients with osteoarthritis treated at the Instituto Mexicano del Seguro Social (IMSS): Comparison of nonsteroidal anti-inflammatory drugs (NSAIDs) vs. cyclooxygenase-2 selective inhibitors

<p>Abstract</p> <p>Background</p> <p>Osteoarthritis (OA) is one of the main causes of disability worldwide, especially in persons >55 years of age. Currently, controversy remains about the best therapeutic alternative for this disease when evaluated from a cost-effectiveness viewpoint. For Social Security Institutions in developing countries, it is very important to assess what drugs may decrease the subsequent use of medical care resources, considering their adverse events that are known to have a significant increase in medical care costs of patients with OA. Three treatment alternatives were compared: celecoxib (200 mg twice daily), non-selective NSAIDs (naproxen, 500 mg twice daily; diclofenac, 100 mg twice daily; and piroxicam, 20 mg/day) and acetaminophen, 1000 mg twice daily. The aim of this study was to identify the most cost-effective first-choice pharmacological treatment for the control of joint pain secondary to OA in patients treated at the Instituto Mexicano del Seguro Social (IMSS).</p> <p>Methods</p> <p>A cost-effectiveness assessment was carried out. A systematic review of the literature was performed to obtain transition probabilities. In order to evaluate analysis robustness, one-way and probabilistic sensitivity analyses were conducted. Estimations were done for a 6-month period.</p> <p>Results</p> <p>Treatment demonstrating the best cost-effectiveness results [lowest cost-effectiveness ratio $17.5 pesos/patient ($1.75 USD)] was celecoxib. According to the one-way sensitivity analysis, celecoxib would need to markedly decrease its effectiveness in order for it to not be the optimal treatment option. In the probabilistic analysis, both in the construction of the acceptability curves and in the estimation of net economic benefits, the most cost-effective option was celecoxib.</p> <p>Conclusion</p> <p>From a Mexican institutional perspective and probably in other Social Security Institutions in similar developing countries, the most cost-effective option for treatment of knee and/or hip OA would be celecoxib.</p

An approximation to a sharp type solution of a density-dependent diffusion equation

In this paper, we use a perturbation method to obtain an approximation to a saddle-saddle heteroclinic trajectory of an autonomous system of ordinary differential equations (ODEs) arising in the equation $u_t= [(u+\epsilon u^2)u_x]_x+u(1-u)$ in the case of travelling wave solutions (t.w.s.): $u(x,t) = \phi (x - ct)$. We compare the approximate form of the solution profile and speed thus obtained with the actual solution of the full model and the calculated speed, respectively

The Speed of Fronts of the Reaction Diffusion Equation

We study the speed of propagation of fronts for the scalar reaction-diffusion equation $u_t = u_{xx} + f(u)$\, with $f(0) = f(1) = 0$. We give a new integral variational principle for the speed of the fronts joining the state $u=1$ to $u=0$. No assumptions are made on the reaction term $f(u)$ other than those needed to guarantee the existence of the front. Therefore our results apply to the classical case $f > 0$ in $(0,1)$, to the bistable case and to cases in which $f$ has more than one internal zero in $(0,1)$.Comment: 7 pages Revtex, 1 figure not include