Global existence of solutions to a magnetohydrodynamic‐omega model

In this paper, some sufficient conditions in terms of the magnetic field are established to guarantee global existence of solutions to a magnetohydrodynamic‐omega model.     

Global existence of classical solutions to a combined chemotaxis-haptotaxis model with logistic source

This paper deals with a mathematical model of cancer invasion of tissue. The model consists of a system of reaction-diffusion-taxis partial differential equations describing interactions between cancer cells, matrix degrading enzymes, and the host tissue. In two space dimensions, we prove global existence and uniqueness of classical solutions to this model for any μ>0 (where μ is the logistic growth rate of cancer cells). The crucial point of proof is to raise the regularity estimate of a solution from L¹(Ω) to L³(Ω×(0,T)) (where Ω⊂R² is some bounded domain and T>0 is some constant). This paper develops new estimate techniques and improves greatly our previous results [Y. Tao, M. Wang, Global solution for a chemotactic-haptotactic model of cancer invasion, Nonlinearity 21 (2008) 2221-2238] in 2 dimensions.     

Global existence of weak solutions to a diffuse interface model for magnetic fluids

This article is devoted to the derivation and analysis of a system of partial differential equations modeling a diffuse interface flow of two Newtonian incompressible magnetic fluids. The system consists of the incompressible Navier–Stokes equations coupled with an evolutionary equation for the magnetization vector and the Cahn–Hilliard equations. We show global in time existence of weak solutions to the system using the time discretization method.     

On the global existence of solutions to an aggregation model

In this paper we consider a reaction-diffusion-chemotaxis aggregation model of Keller-Segel type with a nonlinear, degenerate diffusion. Assuming that the diffusion function f(n) takes values sufficiently large, i.e. takes values greater than the values of a power function with sufficiently high power (f(n)?δnp for all n>0, where δ>0 is a constant), we prove global-in-time existence of weak solutions. Since one of the main features of Keller-Segel type models is the possibility of blow-up of solutions in finite time, we will derive the uniform-in-time boundedness, which prevents the explosion of solutions. The uniqueness of solutions is proved provided that some higher regularity condition on solutions is known a priori. Finally, computational simulation results showing the effect of three different types of diffusion function are presented.     

Global existence of weak solutions for a viscous two-phase model

The purpose of this paper is to explore a viscous two-phase liquid-gas model relevant for well and pipe flow. Our approach relies on applying suitable modifications of techniques previously used for studying the single-phase isothermal Navier-Stokes equations. A main issue is the introduction of a novel two-phase variant of the potential energy function needed for obtaining fundamental a priori estimates. We derive an existence result for weak solutions in a setting where transition to single-phase flow is guaranteed not to occur when the initial state is a true mixture of both phases. Some numerical examples are also included in order to demonstrate characteristic behavior of solutions. In particular, we illustrate how two-phase flow is genuinely different compared to single-phase flow concerning the behavior of an initial mass discontinuity.     

Global existence of solutions to a hyperbolic-parabolic system

In this paper, we investigate the global existence of solutions to a hyperbolic-parabolic model of chemotaxis arising in the theory of reinforced random walks. To get -estimates of solutions, we construct a nonnegative convex entropy of the corresponding hyperbolic system. The higher energy estimates are obtained by the energy method and a priori assumptions.

     

Global existence of the finite energy weak solutions to a nematic liquid crystals model

In this paper, we are concerned with a simplified hydrodynamic equation, proposed by Ericksen and Leslie, modeling the flow of nematic liquid crystals. For a bounded domain in Ropf³, under the assumption that initial density belongs to , we show the global existence of weak solutions to the nematic liquid crystals model with a penalized system. Furthermore, we also obtain the energy inequality for weak solutions. Copyright © 2011 John Wiley & Sons, Ltd.     

Global existence and blowup of solutions to a free boundary problem for mutualistic model

This article is concerned with a system of semilinear parabolic equations with a free boundary, which arises in a mutualistic ecological model. The local existence and uniqueness of a classical solution are obtained. The asymptotic behavior of the free boundary problem is studied. Our results show that the free problem admits a global slow solution if the inter-specific competitions are strong, while if the inter-specific competitions are weak there exist the blowup solution and global fast solution.     

具有常数输入的非自治SIR流行病模型周期解的存在性

利用MAWHIN重合度理论中的延拓定理研究了一类具有常数输入的非自治SIR流行病模型的非平凡周期解的存在性.并用MatLab对其进行了数值模拟,作出了模型的相图和解曲线图形.     

On the existence of optimal solutions in a stochastic control model

An existence result for a stochastic control model with chance constraints, obtained by Christopeit (Ref. 1), is considerably generalized by combining a standard isometry property of Wiener integrals with a well-known lower semicontinuity result for integral functionals.     

The existence of traveling wave front solutions of a model of the Belousov-Zhabotinskii chemical reaction

The boundary value problem $\text{?u}\text{?t′}\text{= u(1 ? u ? rv) +}\text{?}{}^2\text{u}\text{?x′}{}^2$$\text{?v}\text{?t′}\text{= ? buv +}\text{?}{}^2\text{y}\text{?x′}{}^2$ where u(? ∞, t′) = v(∞, t′) = 0 andv(? ∞, t′) = u(∞, t′) = 1 for each t′ > 0 has been proposed by Murray as a model for the Belousov-Zhabotinskii chemical reaction. Here u and v are proportional to the concentrations of bromous acid and bromide ion, respectively. We prove that there is a range of values for b and r over which the boundary value problem has traveling wave front solutions.     

On global existence of solutions to a cross-diffusion system

We consider a strongly coupled nonlinear parabolic system which arises in population dynamics in n-dimensional domains (n?1). We prove the global existence of classical solutions to the system for n<10.     

Global existence of solutions to a coupled coagulation system

We consider a model equations describing the coagulation process of a gas on a surface. The problem is modeled by two coupled equations. The first one is a nonlinear transport equation with bilinear coagulation operator while the second one is a nonlinear ordinary differential equation. The velocity and the boundary condition of the transport equation depend on the supersaturation function satisfying the nonlinear ode. We first prove global existence and uniqueness of solution to the nonlinear transport equation then, we consider the coupled problem and prove existence in the large of solutions to the full coagulation system.     

Global existence of periodic solutions in an infection model

In this paper, a HTLV-I infection model with CTL immune response is considered. Taking the immune delay as a bifurcation parameter we investigate the global existence of periodic solutions of this model which shows existence of multiple periodic solutions theoretically.