Decay Estimates of Heat Transfer to Melton Polymer Flow in Pipes with Viscous Dissipation

In this work, we compare a parabolic equation with an elliptic equation both of which are used in modeling temperature profile of a powerlaw polymer ow in a semi-infinite straight pipe with circular cross section. We show that both models are well-posed and we derive exponential rates of convergence of the two solutions to the same steady state solution away from the entrance. We also show estimates for difference between the two solutions in terms of physical data

Existence of global solution and nontrivial steady states for a system modeling chemotaxis

We consider a reaction-diffusion system modeling chemotaxis, which describes the situation of two species of bacteria competing for the same nutrient. We use Moser-Alikakos iteration to prove the global existence of the solution. We also study the existence of nontrivial steady state solutions and their stability

Coexistence and stability of solutions for a class of reaction-diffusion systems

In this paper we consider the situation of two species of predators competing for one species of prey. We use comparison principles to study the global existence, the existence of non-trivial steady states and their stability

Qualitative analysis of a mathematical model for malaria transmission and its variation

In this article we consider a mathematical model of malaria transmission. We investigate both a reduced model which corresponds to the situation when the infected mosquito population equilibrates much faster than the human population and the full model. We prove that when the basic reproduction number is less than one, the disease-free equilibrium is the only equilibrium and it is locally asymptotically stable and if the reproduction number is greater than one, the disease-free equilibrium becomes unstable and an endemic equilibrium emerges and it is asymptotically stable. We also prove that, when the reproduction number is greater than one, there is a minimum wave speed $c^*$ such that a traveling wave solution exists only if the wave speed c satisfies $c\geq c^*$. Finally, we investigate the relationship between spreading speed and diffusion coefficients. Our results show that the movements of mosquito population and human population will speed up the spread of the disease

The Effects of Classical Trapping on the Control of Malaria Transmission

This paper investigates the effects of classical trapping on the control of malaria transmission. The Ross-Macdonald model is modified and a trapping probability function is introduced to construct a partial differential equation (PDE) system. The proof of existence and uniqueness of solution of density functions to the PDE system is given, numerical simulation results based on Gaussian distribution and exponential distribution are obtained for the solutions, and graphical representations of solutions are shown and interpreted

The Effects of Classical Trapping on the Control of Malaria Transmission

This paper investigates the effects of classical trapping on the control of malaria transmission. The Ross-Macdonald model is modified and a trapping probability function is introduced to construct a partial differential equation (PDE) system. The proof of existence and uniqueness of solution of density functions to the PDE system is given, numerical simulation results based on Gaussian distribution and exponential distribution are obtained for the solutions, and graphical representations of solutions are shown and interpreted

An improved method for estimating ice line for zonal energy balance climate models

In this article we consider an energy balance climate model. For a given ice line, we use spectral method to derive an approximation of the solution. Then we propose a method to update the ice line and to derive an updated approximation of the solution. We compare the difference between the approximation with fixed ice line and the approximation with updated ice line by looking at the temperature profile at some specific locations and times. The significance of the method to update the ice line is that it is model free. Therefore, it can be used in other climate models