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1.
We consider an integral equation of the radiative transfer type stated in the interval [0,τ0] with the length τ01. We construct an asymptotic solution of the problem and we give a method transforming this problem to some similar problems set in the interval with the length dτ0. Error estimates are proved. 相似文献
2.
Wenzhen GanZhigui Lin 《Applied Mathematical Modelling》2012,36(3):989-996
This paper deals with a two species model with Schoener’s competitive interaction. The existence and the asymptotic behavior of T-periodic solutions for the periodic system of quasilinear parabolic equations under nonlinear boundary conditions are given by using upper and lower solutions and corresponding iteration. The numerical simulations are also presented to illustrate our result. It is shown that periodic solutions may exist if the inter-specific competition rates are weak. 相似文献
3.
In this paper, the competitor-competitor-mutualist three-species Lotka-Volterra model is discussed. Firstly, by Schauder fixed point theory, the coexistence state of the strongly coupled system is given. Applying the method of upper and lower solutions and its associated monotone iterations, the true solutions are constructed. Our results show that this system possesses at least one coexistence state if cross-diffusions and cross-reactions are weak. Secondly, the existence and asymptotic behavior of T-periodic solutions for the periodic reaction-diffusion system under homogeneous Dirichlet boundary conditions are investigated. Sufficient conditions which guarantee the existence of T-periodic solution are also obtained. 相似文献
4.
Global warming results in a slow expansion of habitat range of mosquitoes, an important vector of dengue virus. To understand the impact of this changing environment on the transmission of dengue virus, we develop a dengue model on a growing domain under the framework of reaction diffusion equations. By overcoming some difficulties of dynamical behaviors caused by diffusion terms with variable-dependent coefficients, we investigate the stabilities of the disease-free and endemic equilibria in terms of the associated basic reproduction number. Comparing our dengue model on a growing domain to the model on a fixed domain in terms of the basic reproduction number, we conclude that habitat expansion resulting from global warming catalyzes the spread of dengue fever, and it is negative to the control of dengue fever. Finally, numerical simulations are performed and show a good agreement with our analytical results. 相似文献
5.
Yeping Li 《Journal of Differential Equations》2006,225(1):134-167
In this paper, a multidimensional nonisentropic hydrodynamic model for semiconductors with the nonconstant lattice temperature is studied. The model is self-consistent in the sense that the electric field, which forms a forcing term in the momentum equation, is determined by the coupled Poisson equation. Global existence to the Cauchy problem for the multidimensional nonisentropic hydrodynamic semiconductor model with the small perturbed initial data is established, and the asymptotic behavior of these smooth solutions is investigated, namely, that the solutions converge to the general steady-state solution exponentially fast as t→+∞ is obtained. Moreover, the existence and uniqueness of the stationary solutions are investigated. 相似文献
6.
An integrodifference model describing the reproduction and dispersal of a population is introduced to investigate the evolution of dispersal in a spatially periodic habitat. The dispersal is determined by a kernel function, and the dispersal strategy is defined as the probability of population individuals’ moving to a different habitat. Both conditional and unconditional dispersal strategies are investigated, the distinction being whether dispersal depends on local environmental conditions. For competing unconditional dispersers, we prove that the population with the smaller dispersal probability always prevails. Alternatively, for conditional dispersers, it is shown that the strategy known as ideal free dispersal is both sufficient and necessary for evolutionary stability. These results extend those in the literature for discrete diffusion models in finite patchy landscapes and from reaction–diffusion models. 相似文献
7.
The effect of population dispersal among n patches on the spread of a disease is investigated. Population dispersal does not destroy the uniqueness of a disease free equilibrium and its attractivity when the basic reproduction number of a disease R0<1. When R0>1, the uniqueness and global attractivity of the endemic equilibrium can be obtained if dispersal rates of susceptible individuals and infective individuals are the same or very close in each patch. However, numerical calculations show that population dispersal may result in multiple endemic equilibria and even multi-stable equilibria among patches, and also may result in the extinction of a disease, even though it cannot be eradicated in each isolated patch, provided the basic reproduction numbers of isolated patches are not very large. 相似文献
8.
This paper is concerned with the spreading speed for a nonlocal dispersal vaccination model with general incidence. We first prove the existence and uniform boundedness of solutions for this model by using the Schauder’s fixed point theorem. Then, applying comparison principle, we establish the existence of spreading speed for the infective individuals. According to our result, one can see that the spreading speed coincides with the critical speed of traveling wave solution connecting the disease-free and endemic equilibria. In addition, the diffusion rate of the infected individuals can increase the spread of infectious diseases, while the vaccination rate reduces the spread of infectious diseases. 相似文献
9.
In this paper we study a simplified transient energy-transport model in semiconductors with a general conductivity and the Dirichlet boundary conditions on an interval. By using a new iterative scheme, we prove the global existence and uniqueness of strong solutions provided that the variation of the temperature is small. Also, the existence and stability of stationary solutions are proved if the temperature is large. 相似文献
10.
This paper is concerned with traveling wave solutions of a nonlocal dispersal SIR epidemic model. The existence and nonexistence of traveling wave solutions are determined by the basic reproduction number and the minimal wave speed. This threshold dynamics are proved by Schauder’s fixed point theorem and the Laplace transform. The main difficulties are that the semiflow generated by the model does not have the order-preserving property and the solutions lack of regularity. 相似文献
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12.
Shakhov model is a relaxation approximation of the Boltzmann equation proposed to overcome the deficiency of the original BGK model, namely, the incorrect production of the Prandtl number. In this paper, we address the existence and the asymptotic stability of the Shakhov model when the initial data is a small perturbation of global equilibrium. We derive a dichotomy in the coercive estimate of the linearized relaxation operator between zero and non-zero Prandtl number, and observe that the linearized relaxation operator is more degenerate in the former case. To remove such degeneracy and recover the full coercivity, we consider a micro–macro system that involves an additional non-conservative quantity related to the heat flux. 相似文献
13.
In this paper we examine the Akian, Menaldi and Sulem (1996) model for the optimal management of a portfolio, when there are transaction costs which are equal to a fixed percentage of the amount transacted. We analyse this model in the realistic limit of small transaction costs. Although the full problem is a free boundary diffusion problem in as many dimensions as there are assets in the portfolio, we find explicit solutions for the optimal trading policy in this limit. This makes the solution for a realistically large number of assets a practical possibility. 相似文献
14.
Peiyuan Meng 《Journal of Mathematical Analysis and Applications》2010,361(2):322-331
In this note, we consider a one-dimensional bipolar Euler-Poisson system (hydrodynamic model). This system takes the form of Euler-Poisson with electric field and frictional damping added to the momentum equations. When n+≠n−, paper [I. Gasser, L. Hsiao, H.-L. Li, Large time behavior of solutions of the bipolar hydrodynamical model for semiconductors, J. Differential Equations 192 (2003) 326-359] discussed the asymptotic behavior of small smooth solutions to the Cauchy problem of the one-dimensional bipolar Euler-Poisson system. Subsequent to [I. Gasser, L. Hsiao, H.-L. Li, Large time behavior of solutions of the bipolar hydrodynamical model for semiconductors, J. Differential Equations 192 (2003) 326-359], we investigate the asymptotic behavior of solutions to the Cauchy problem with , and obtain the optimal convergence rate toward the constant state . We accomplish the proofs by energy estimates and the decay rates of fundamental solutions of the heat-type equations. 相似文献
15.
In this paper, the authors study the asymptotic behavior of solutions of second-order neutral type difference equations of the form
Δ2(yn+pyn−k)+f(n,yn−ℓ)=0,n