A document by Hadi Babaei. Click on the document to view its contents.

This paper is concerned with a West Nile virus (WNv) model on a growing domain, which accounts for habitat expansion of mosquitoes because of climate warming. We aim to understand the relationship of the growing rate and the transmission risk of WNv. The basic reproduction number, which is related to the growing rate and diffusion rate, is introduced through spectral theory. The conditions to determine whether the virus vanishes or spreads are deduced.The obtained results reveal that domain growth leads to increased risk of infection, and is detrimental to the control and prevention of WNv. To verify the feasibility of our analytical results on the long time behavior of WNv, some numerical simulations are given.

We are interested in defining new energy functionals and solving them by using the variational approach method. That is, we aim to define a new class of elastic curves in the three-dimensional ordinary space. We further improve an alternative method to find critical points of the bending energy functionals acting on a class of magnetic curves. Then, we classify these critical curves as elastic magnetic curves of the Frenet-Serret vector family. Moreover, we investigate the dynamics of the elastic magnetic curves of ferromagnetic and superparamagnetic models and discuss their numerical and analytical analysis.

In this paper, for the first time, the distributed order time-fractional forced Korteweg-de Vries equation is studied. We use a numerical method based on the shifted Legendre operational matrix of distributed order fractional derivative with Tau method to find approximate solution of distributed order forced Korteweg-de Vries equation. This shifted Legendre operational matrix of distributed order fractional derivative with Tau method are used to reduce the solution of the distributed order time-fractional forced Korteweg-de Vries equations to a system of algebraic equations. An error analysis and convergence are obtained. Finally, to display the applicability and validity of the numerical method some examples are implemented.

In this work, we develop a new mathematical model to evaluate the impact of drug therapies on autoimmunity disease. We describe the immune system interactions at the cellular level, using the kinetic theory approach, by considering self-antigen presenting cells, self-reactive T cells, immunosuppressive cells and Interleukin-2 (IL-2) cytokines. The drug therapy consists of an intake of Interleukin-2 cytokines which boosts the effect of immunosuppressive cells on the autoimmune reaction. We also derive the macroscopic model relative to the kinetic system and study the wellposedness of the Cauchy problem for the corresponding system of equations. We formulate an optimal control problem relative to the model so that the quantity of both the self-reactive T cells that are produced in the body and the Interleukin-2 cytokines that are administrated is simultaneously minimized. Moreover, we perform some numerical tests in view of investigating optimal treatment strategies and the results reveal that the optimal control approach provides good-quality approximate solutions and shows to be a valuable procedure in identifying optimal treatment strategies.

In this paper, we study blow-up phenomena of the following p-Laplace type nonlinear parabolic equations under nonlinear mixed boundary conditions and u = 0 on Γ₂ × (0, t*) such that Γ₁ ∪ Γ₂ = ∂Ω, where f and h are real-valued C¹-functions. To discuss blow-up solutions, we introduce new conditions: For each x ∈ Ω, z ∈ ∂Ω, t > 0, u > 0, and v > 0, for some constants α, β₁, β₂, γ₁, γ₂, and δ satisfying where ρm := infw > 0ρ(w), P(v)=∫₀vρ(w)dw, F(x, t, u)=∫₀uf(x, t, w)dw, and H(x, t, u)=∫₀uh(x, t, w)dw. Here, λR is the first Robin eigenvalue and λS is the first Steklov eigenvalue for the p-Laplace operator, respectively.

Since December 2019 that coronavirus pandemic (COVID-19) has hit the world, with over 13 million cases recorded, only a little above 4.67 percent of the cases have been recorded in the continent of Africa. The percentage of cases in Africa rose significantly from 2 percent in the month of May 2020 to above 4.67 percent by the end of July 15, 2020. This rapid increase in the percentage indicates a need to study the transmission, control strategy, and the dynamics of COVID-19 in Africa continent. In this study, a nonlinear mathematical model to investigate the impact of asymptomatic cases on the transmission dynamics of COVID-19 in Africa is proposed. The model is analyzed, the reproduction number is obtained, the local, as well as the global, asymptotic stability of the equilibria were established. We investigate the existence of backward bifurcation and we present the numerical simulations to verify our theoretical results.

The article is concerned with the analytical solution to the integro-differential system of balance and kinetic equations that describe the crystal growth phenomenon in a binary system for various nucleation kinetics. The effect of impurity concentration on the evolutionary behavior of crystals is shown. The nonlinear dynamics of a supercooled binary melt is studied with allowance for the withdrawal mechanism of product crystals from a metastable liquid of the crystallizer.

The ecological consciousness has driven developed societies to explore alterna- tives to the growing need for energy and the consequent increase in waste pro- duction. The adjustment towards the waste recovery and their transformation into energy, by various processes, is then necessary. However, so far the domain has not benefited much from a mathematical modeling approach. The main con- tribution of this work consists of building a bio-economic model describing the problem of a potential investor who aims to maximize his net profit generated by selling the produced energy from the household waste transformation. We first study the evolution of a waste stock, the energy quantity produced and the capital dedicated to the transformation process in a giving landfill and recovery center. Then we insert decision variables to this dynamic which are both the investment and the part of waste to be treated. This leads to an optimal control problem which we solve by the deductive method. The resulted solution is then illustrated by some numerical simulations. This investment policy would be to support the decision-makers to go toward investment in this activity.

The present study concerns the Stokes flow of a micropolar fluid through a porous cylinder which axis is perpendicular to the plane of flow. Stream functions, velocities, fluid pressures and stresses are evaluated for corresponding fluid flow regions. Streamlines for various values of different parameters are plotted and discussed. Also, the fluid velocity vector and microrotation vector for inside and outside the cylinder are plotted for the different values of the viscosity coefficients and discussed for boundary conditions with continuity of couple stress / continuity of tangential stress. A comparative study of the streamlines, velocity components, microrotation components is presented for two types of the boundary value problems.

In this paper, we give a new higher dimensional Hermite-Hadamard inequality for a function $f:\prod\limits_{i=1}^n[a_i,b_i]\subset\mathbb{R}^n\rightarrow\mathbb{R}$ which is semiconvex of rate $(k_1,k_2,…,k_n)$ on the co-ordinates. This generalizes some existing results on Hermite-Hadamard inequalities of S.S. Dragomir. In addition, we explain the Hermite-Hadamard inequality from the point of view of optimal mass transportation with cost function $c(x,y):=f(y-x)+\sum_{i=1}^n\frac{k_i}{2}\big|x_i-y_i\big|^2$, where $f(\cdot):\prod\limits_{i=1}^n[a_i,b_i]\rightarrow[0,\infty)$ is semiconvex of rate $(k_1,k_2,…,k_n)$ on the co-ordinates and $x=(x_1,x_2,…,x_n)$, $y=(y_1,y_2,…,y_n)\in\prod\limits_{i=1}^n[a_i,b_i]$. Furthermore, by using the higher dimensional Hermite-Hadamard inequality, we compare the transport cost in different transport models on the sphere $\mathbb{S}^2$.

The paper is concerned with the multiple solutions of a nonhomogeneous elliptic system with critical exponent over a non-contractible domain, precisely, a smooth bounded annular domain. We prove the existence of four solutions using variational methods and Lusternik-Schnirelmann theorey, when the inner hole of the annulus is sufficiently small.

In this work, the Lie symmetry theory is used to study the propagation of waves in an elastic string with electric currents in a static magnetic field. Both linear and nonlin- ear cases of the governing equations of string motion are analyzed. The classification problem of finding the principal admitted Lie groups of symmetries is solved. Some invariant analytical solutions are constructed. The physics of invariant solutions is interpreted when it is possible.

In this paper, we prove the weighted Lorentz and weighted Orlicz estimates for the weak solutions to the higher order parabolic systems with the leading coefficients satisfying a small BMO norm condition. As a byproduct, we obtain the weighted estimates for the higher order elliptic systems.

Based on the least square method, we proposed a new algorithm to obtain the solution of the second kind regular and weakly singular Volterra-Fredholm integral equations in reproducing kernel spaces. The stability and uniform convergence of the algorithm are investigated in details. Numerical experiments verify the theoretical findings. Meanwhile this method is also applicable to the nonlinear Volterra integral equations. Test problems which have non-smooth solutions are also considered and our proposed method is efficient as some recent Krylov subspace methods such as LSQR and LSMR.

The Markov evolution is studied of an infinite age-structured population of migrants arriving in and departing from a continuous habitat $X \subseteq\mathds{R}^d$ – at random and independently of each other. Each population member is characterized by its age $a\geq 0$ (time of presence in the population) and location $x\in X$. The population states are probability measures on the space of the corresponding marked configurations. The result of the paper is constructing the evolution $\mu_0 \to \mu_t$ of such states by solving a standard Fokker-Planck equation for this models. We also found a stationary state $\mu$ existing if the emigration rate is separated away from zero. It is then shown that $\mu_t$ weakly converges to $\mu$ as $t\to +\infty$.

In this paper, we consider a class of non-cooperative critical nonlocal equation system with variable exponents of the form: $$ \left\{ \begin{array}{lll} -(-\Delta)_{p(\cdot,\cdot)}^su - |u|^{p(x)-2}u = F_u(x,u,v) + |u|^{q(x)-2}u, \quad &\mbox{in}\,\,\mathbb{R}^N,\\ (-\Delta)_{p(\cdot,\cdot)}^sv + |v|^{p(x)-2}v = F_v(x,u,v) + |v|^{q(x)-2}u, \quad &\mbox{in}\,\,\mathbb{R}^N,\\ u, v \in W^{s,p(\cdot,\cdot)}(\mathbb{R}^N), \end{array}\right. $$ where $\nabla F = (F_u, F_v)$ is the gradient of a $C^1$-function $F: \mathbb{R}^N\times \mathbb{R}^2 \rightarrow \mathbb{R}^+$ with respect to the variable $(u, v) \in \mathbb{R}^2$. We also assume that$\{x \in \mathbb{R}^N: q(x) = p_s^\ast(x)\} \neq \emptyset$, here $p_s^\ast(x)=Np(x,x)/(N-sp(x,x))$ is the critical Sobolev exponent for variable exponents. With the help of the Limit index theory and the concentration-compactness principles for fractional Sobolev spaces with variable exponents, we establish the existence of infinitely many solutions for the problem under the suitable conditions on the nonlinearity.

In this paper, we establish the existence and uniqueness of a time periodic solution to the full compressible quantum Euler equations. First, we prove the existence of time periodic solutions under some smallness assumptions imposed on the external force in a periodic domain by a regularized approximation scheme and the Leray-Schauder degree theory. Then the result is generalized to $\mathbb{R}^{3}$ by adapting a limiting method and a diagonal argument. The uniqueness of the time periodic solutions is also given. Compared to classical Euler equations, the third-order quantum spatial derivatives are considered which need some elaborated treatments thereof in obtaining the highest-order energy estimates.