## Recursos de colección

#### Project Euclid (Hosted at Cornell University Library) (203.209 recursos)

International Journal of Differential Equations

1. #### High-Speed Transmission in Long-Haul Electrical Systems

Juárez-Campos, Beatriz; Kaikina, Elena I.; Naumkin, Pavel I.; Ruiz-Paredes, Héctor Francisco
We study the equations governing the high-speed transmission in long-haul electrical systems $i{\partial }_{t}u-(\mathrm{1}/\mathrm{3}){|{\partial }_{x}|}^{\mathrm{3}}u=i\lambda {\partial }_{x}({|u|}^{\mathrm{2}}u)$ , $(t,x)\in {\mathbb{R}}^{+}\times\mathbb{R}$ , $u(\mathrm{0},x)={u}_{\mathrm{0}}(x)$ , $x\in \mathbb{R},$ where $\lambda \in \mathbb{R},\text{\hspace\{0.17em\}\hspace\{0.17em\}}{|{\partial }_{x}|}^{\alpha }={\mathcal{F}}^{-\mathrm{1}}{|\xi |}^{\alpha }\mathcal{F}$ , and $\mathcal{F}$ is the Fourier transformation. Our purpose in this paper is to obtain the large time asymptotics for the solutions under the nonzero mass condition $\int {u}_{\mathrm{0}}(x)dx\ne \mathrm{0}.$

2. #### Applications of Parameterized Nonlinear Ordinary Differential Equations and Dynamic Systems: An Example of the Taiwan Stock Index

Li, Meng-Rong; Chiang-Lin, Tsung-Jui; Lee, Yong-Shiuan
Considering the phenomenon of the mean reversion and the different speeds of stock prices in the bull market and in the bear market, we propose four dynamic models each of which is represented by a parameterized ordinary differential equation in this study. Based on existing studies, the models are in the form of either the logistic growth or the law of Newton’s cooling. We solve the models by dynamic integration and apply them to the daily closing prices of the Taiwan stock index, Taiwan Stock Exchange Capitalization Weighted Stock Index. The empirical study shows that some of the models fit...

3. #### An Analytical and Approximate Solution for Nonlinear Volterra Partial Integro-Differential Equations with a Weakly Singular Kernel Using the Fractional Differential Transform Method

Ghoochani-Shirvan, Rezvan; Saberi-Nadjafi, Jafar; Gachpazan, Morteza
An analytical-approximate method is proposed for a type of nonlinear Volterra partial integro-differential equations with a weakly singular kernel. This method is based on the fractional differential transform method (FDTM). The approximate solutions of these equations are calculated in the form of a finite series with easily computable terms. The analytic solution is represented by an infinite series. We state and prove a theorem regarding an integral equation with a weak kernel by using the fractional differential transform method. The result of the theorem will be used to solve a weakly singular Volterra integral equation later on.

4. #### On the Global Dynamics of a Vector-Borne Disease Model with Age of Vaccination

Ouaro, Stanislas; Traoré, Ali
We study a vector-borne disease with age of vaccination. A nonlinear incidence rate including mass action and saturating incidence as special cases is considered. The global dynamics of the equilibria are investigated and we show that if the basic reproduction number is less than 1, then the disease-free equilibrium is globally asymptotically stable; that is, the disease dies out, while if the basic reproduction number is larger than 1, then the endemic equilibrium is globally asymptotically stable, which means that the disease persists in the population. Using the basic reproduction number, we derive a vaccination coverage rate that is required...

5. #### Well-Posedness and Numerical Study for Solutions of a Parabolic Equation with Variable-Exponent Nonlinearities

Al-Smail, Jamal H.; Messaoudi, Salim A.; Talahmeh, Ala A.
We consider the following nonlinear parabolic equation: ${u}_{t}-\mathrm{d}\mathrm{i}\mathrm{v}(|\nabla u{|}^{p(x)-\mathrm{2}}\nabla u)=f(x,t)$ , where $f:\mathrm{\Omega }\times(\mathrm{0},T)\to \mathbb{R}$ and the exponent of nonlinearity $p(·)$ are given functions. By using a nonlinear operator theory, we prove the existence and uniqueness of weak solutions under suitable assumptions. We also give a two-dimensional numerical example to illustrate the decay of solutions.

6. #### Spatiotemporal Dynamics of an HIV Infection Model with Delay in Immune Response Activation

Maziane, Mehdi; Hattaf, Khalid; Yousfi, Noura
We propose and analyse an human immunodeficiency virus (HIV) infection model with spatial diffusion and delay in the immune response activation. In the proposed model, the immune response is presented by the cytotoxic T lymphocytes (CTL) cells. We first prove that the model is well-posed by showing the global existence, positivity, and boundedness of solutions. The model has three equilibria, namely, the free-infection equilibrium, the immune-free infection equilibrium, and the chronic infection equilibrium. The global stability of the first two equilibria is fully characterized by two threshold parameters that are the basic reproduction number ${R}_{\mathrm{0}}$ and the CTL immune response...

7. #### Uniqueness Results for Higher Order Elliptic Equations in Weighted Sobolev Spaces

Caso, Loredana; Di Gironimo, Patrizia; Monsurrò, Sara; Transirico, Maria
We prove some uniqueness results for the solution of two kinds of Dirichlet boundary value problems for second- and fourth-order linear elliptic differential equations with discontinuous coefficients in polyhedral angles, in weighted Sobolev spaces.

8. #### Qualitative Analysis of a Generalized Virus Dynamics Model with Both Modes of Transmission and Distributed Delays

Hattaf, Khalid; Yousfi, Noura
We propose a generalized virus dynamics model with distributed delays and both modes of transmission, one by virus-to-cell infection and the other by cell-to-cell transfer. In the proposed model, the distributed delays describe (i) the time needed for infected cells to produce new virions and (ii) the time necessary for the newly produced virions to become mature and infectious. In addition, the infection transmission process is modeled by general incidence functions for both modes. Furthermore, the qualitative analysis of the model is rigorously established and many known viral infection models with discrete and distributed delays are extended and improved.

9. #### Mathematical Modeling of the Adaptive Immune Responses in the Early Stage of the HBV Infection

The aim of this paper is to study the early stage of HBV infection and impact delay in the infection process on the adaptive immune response, which includes cytotoxic T-lymphocytes and antibodies. In this stage, the growth of the healthy hepatocyte cells is logistic while the growth of the infected ones is linear. To investigate the role of the treatment at this stage, we also consider two types of treatment: interferon- $\mathrm{\alpha }$ (IFN) and nucleoside analogues (NAs). To find the best strategy to use this treatment, an optimal control approach is developed to find the possibility of having a...

10. #### Convergent Power Series of $\mathrm{sech}(x)$ and Solutions to Nonlinear Differential Equations

Al Khawaja, U.; Al-Mdallal, Qasem M.
It is known that power series expansion of certain functions such as $\mathrm{sech}(x)$ diverges beyond a finite radius of convergence. We present here an iterative power series expansion (IPS) to obtain a power series representation of $\mathrm{sech}(x)$ that is convergent for all $x$ . The convergent series is a sum of the Taylor series of $\mathrm{sech}(x)$ and a complementary series that cancels the divergence of the Taylor series for $x\ge \pi /\mathrm{2}$ . The method is general and can be applied to other functions known to have finite radius of convergence, such as $\mathrm{1}/(\mathrm{1}+{x}^{\mathrm{2}})$ . A straightforward application of this...

11. #### Existence of Global Solutions for Nonlinear Magnetohydrodynamics with Finite Larmor Radius Corrections

Elsrrawi, Fariha; Hattori, Harumi
We discuss the existence of global solutions to the magnetohydrodynamics (MHD) equations, where the effects of finite Larmor radius corrections are taken into account. Unlike the usual MHD, the pressure is a tensor and it depends on not only the density but also the magnetic field. We show the existence of global solutions by the energy methods. Our techniques of proof are based on the existence of local solution by semigroups theory and a priori estimate.

12. #### Linearization of Fifth-Order Ordinary Differential Equations by Generalized Sundman Transformations

Suksern, Supaporn; Naboonmee, Kwanpaka
In this article, the linearization problem of fifth-order ordinary differential equation is presented by using the generalized Sundman transformation. The necessary and sufficient conditions which allow the nonlinear fifth-order ordinary differential equation to be transformed to the simplest linear equation are found. There is only one case in the part of sufficient conditions which is surprisingly less than the number of cases in the same part for order 2, 3, and 4. Moreover, the derivations of the explicit forms for the linearizing transformation are exhibited. Examples for the main results are included.

13. #### The Impact of Price on the Profits of Fishermen Exploiting Tritrophic Prey-Predator Fish Populations

Bentounsi, Meriem; Agmour, Imane; Achtaich, Naceur; El Foutayeni, Youssef
We define and study a tritrophic bioeconomic model of Lotka-Volterra with a prey, middle predator, and top predator populations. These fish populations are exploited by two fishermen. We study the existence and the stability of the equilibrium points by using eigenvalues analysis and Routh-Hurwitz criterion. We determine the equilibrium point that maximizes the profit of each fisherman by solving the Nash equilibrium problem. Finally, following some numerical simulations, we observe that if the price varies, then the profit behavior of each fisherman will be changed; also, we conclude that the price change mechanism improves the fishing effort of the fishermen.

14. #### Modeling and Analysis of Integrated Pest Control Strategies via Impulsive Differential Equations

Páez Chávez, Joseph; Jungmann, Dirk; Siegmund, Stefan
The paper is concerned with the development and numerical analysis of mathematical models used to describe complex biological systems in the framework of Integrated Pest Management (IPM). Established in the late 1950s, IPM is a pest management paradigm that involves the combination of different pest control methods in ways that complement one another, so as to reduce excessive use of pesticides and minimize environmental impact. Since the introduction of the IPM concept, a rich set of mathematical models has emerged, and the present work discusses the development in this area in recent years. Furthermore, a comprehensive parametric study of an...

15. #### Optimization of the Two Fishermen’s Profits Exploiting Three Competing Species Where Prices Depend on Harvest

Agmour, Imane; Bentounsi, Meriem; Achtaich, Naceur; El Foutayeni, Youssef
Bioeconomic modeling of the exploitation of biological resources such as fisheries has gained importance in recent years. In this work we propose to define and study a bioeconomic equilibrium model for two fishermen who catch three species taking into consideration the fact that the prices of fish populations vary according to the quantity harvested; these species compete with each other for space or food; the natural growth of each species is modeled using a logistic law. The main purpose of this work is to define the fishing effort that maximizes the profit of each fisherman, but all of them have...

16. #### Finite Time Synchronization of Extended Nonlinear Dynamical Systems Using Local Coupling

Acosta, A.; García, P.; Leiva, H.; Merlitti, A.
We consider two reaction-diffusion equations connected by one-directional coupling function and study the synchronization problem in the case where the coupling function affects the driven system in some specific regions. We derive conditions that ensure that the evolution of the driven system closely tracks the evolution of the driver system at least for a finite time. The framework built to achieve our results is based on the study of an abstract ordinary differential equation in a suitable Hilbert space. As a specific application we consider the Gray-Scott equations and perform numerical simulations that are consistent with our main theoretical results.

17. #### Global Dynamics of a Periodic SEIRS Model with General Incidence Rate

Ávila-Vales, Eric; Rivero-Esquivel, Erika; García-Almeida, Gerardo Emilio
We consider a family of periodic SEIRS epidemic models with a fairly general incidence rate of the form $Sf(I)$ , and it is shown that the basic reproduction number determines the global dynamics of the models and it is a threshold parameter for persistence of disease. Numerical simulations are performed using a nonlinear incidence rate to estimate the basic reproduction number and illustrate our analytical findings.

18. #### Global Dynamics of a Periodic SEIRS Model with General Incidence Rate

Ávila-Vales, Eric; Rivero-Esquivel, Erika; García-Almeida, Gerardo Emilio
We consider a family of periodic SEIRS epidemic models with a fairly general incidence rate of the form $Sf(I)$ , and it is shown that the basic reproduction number determines the global dynamics of the models and it is a threshold parameter for persistence of disease. Numerical simulations are performed using a nonlinear incidence rate to estimate the basic reproduction number and illustrate our analytical findings.

19. #### The Morbidity of Multivariable Grey Model MGM$(\mathrm 1,m)$

Wang, Haixia; Zhao, Lingdi; Hu, Mingzhao
This paper proposes the morbidity of the multivariable grey prediction MGM$(\mathrm 1,m)$ model. Based on the morbidity of the differential equations, properties of matrix, and Gerschgorin Panel Theorem, we analyze the factors that affect the morbidity of the multivariable grey model and give a criterion to justify the morbidity of MGM$(\mathrm 1,m)$. Finally, an example is presented to illustrate the practicality of our results.

20. #### The Morbidity of Multivariable Grey Model MGM$(\mathrm 1,m)$

Wang, Haixia; Zhao, Lingdi; Hu, Mingzhao
This paper proposes the morbidity of the multivariable grey prediction MGM$(\mathrm 1,m)$ model. Based on the morbidity of the differential equations, properties of matrix, and Gerschgorin Panel Theorem, we analyze the factors that affect the morbidity of the multivariable grey model and give a criterion to justify the morbidity of MGM$(\mathrm 1,m)$. Finally, an example is presented to illustrate the practicality of our results.

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