In this paper, we deal with the asymptotic behaviour of a semiconductor Boltzmann equation by using the sigma convergence method. We first prove that the scaled model is well-posed in the usual Lebesgue space of square integrable functions, and we perform the a priori estimates. Then, assuming that the coefficients of the model are highly oscillating in space variable, we show that in the non-vanishing flux case, the homogenized problem is equivalent at first order, to a hyperbolic process modified by a perturbation of viscosity, and the diffusion term appears at second order. In the vanishing flux case, we obtain a diffusion model.

This paper investigates the Maxwell-Boltzmann system in the framework of a Bianchi type III space-time. We conduct a rigorous mathematical analysis of the system, emphasizing its structural properties, functional setting, and energy estimates. By employing a combination of the Faedo-Galerkin method and the standard iteration technique, we establish the local-in-time existence and uniqueness of a solution with good regularity. Our approach carefully integrates the geometric constraints imposed by the Bianchi type III background, ensuring a well-posed formulation of the problem. These results contribute to a broader study of the relativistic kinetic theory in anisotropic cosmological models.

We study the Einstein-Yang-Mills-Higgs (EYMH) system with a positive cosmological constant in the Bianchi type I space-time with locally rotational symmetry (LRS). In particular, we consider the nonlinear interaction of the Higgs field with the Yang-Mills field coupled to an unknown gravitational field. For the considered model, from certain additional conditions (the temporal gauge and some symmetries), we derive the conservation laws for the field equations and we then deduce the exact formulation of equations in the geometric framework. Furthermore, using an iterative approch and some mathematical analysis tools, we study the above system of equations. We then establish a global existence result for the homogeneous solution and we analyse its asymptotic behaviour.

This paper provide evidence of the existence and uniqueness result for the viscosity solutions of inhomogeneous Vlasov equation. we consider the Cauchy-Dirichlet problem for the relativistic Vlasov equation with near vacuum initial data where the distribution function depends on the time, the position, the momentum and the non-Abelian charge of particles. We consider this equation on aSchwarzschild outer space-time with Yang-Mills field.

We prove, in this paper, the well-posedness and nonnegativity of the regular solution of the relativistic Boltzmann equation in the presence of a given electromagnetic field, taking as background a Lorentzian space-time which is of type Bianchi I with locally rotational symmetry.

We prove a local in time existence theorem to a Cauchy problem for the coupled Yang- Mills-Boltzmann system in Bianchi type 1 space-time background.

We consider in this work the Boltzmann equation in the presence of a Yang-Mills fields in temporal gauge, which generalizes to the non-Abelian case the electromagnetic field. We prove, using the method presented by N. Nout-chegueme and R. D. Ayissi [2], a local in time existence and uniqueness theorem for the regular solutions.

The paper deals with the homogenization of linear Boltzmann equations by the means of the sigma-convergence method. Replacing the classical periodicity hypothesis on the coefficients of the collision operator by an abstract assumption covering a great variety of physical behaviours, we prove that the density of the particles converges to the solution of a drift-diffusion equation. We then illustrate this abstract setting by working out a few concrete homogenization problems such as the periodic one, the almost periodic one and others. To achieve our goal, we use the Krein–Rutman theorem for locally convex spaces together with the Fredholm alternative to solve the so-called corrector problem.

The initial cases of novel coronavirus (COVID-19) were identified in most West African countries between late February and early March of 2020. But it is only after March 15, 2020 that the number of cases started rising significantly in these countries. This study analyzes the transmission dynamics of the outbreak in West Africa nearly 5 months after the effective onset. We focus on Cameroon, Ghana, Guinea and Nigeria, which are the four West African countries with the highest numbers of infected cases. We combine models of mathematical epidemiology and publicly available data to estimate the main disease transmission characteristics. In particular, we estimate the initial doubling time, the peak time, the peak rate, the final size and the short-term transmission forecasts of the COVID-19 epidemic for these countries. Policy implications for the effectiveness of control measures and for assessing the potential impact on public health in West Africa are discussed.

We consider in this work the Boltzmann equation with absorption term in the presence of an external field which is of Yang-Mills type, on a Bianchi type 1 space-time. Such an equation governs the evolution with collisions of plasmas, for instance of quarks and gluons (quagma), where non-Abelian Yang-Mills field replaces the usual electromagnetic field. A local in time existence and uniqueness result for the classical solution is established, using a suitable combination of Faedo Galerkin method and the standard iteration method. We also prove the well-posedness of the solution.

In this paper, the method of vanishing viscosity described by Evans [10] is used to prove, the existence and uniqueness theorems for the viscosity solution of the Vlasov equation in the presence of a Yang-Mills field in temporal gauge. Such equation governs the evolution without collisions of plasmas, for instance of quarks and gluons (quagmas), where non Abelian gauge fields and Yang-Mills charges replace the usual electromagnetic field and electric charges.

We study the multiscale homogenization of a nonlinear hyperbolic equation in a periodic setting. We obtain an accurate homogenization result. We also show that as the nonlinear term depends on the microscopic time variable, the global homogenized problem thus obtained is a system consisting of two hyperbolic equations. It is also shown that in spite of the presence of several time scales, the global homogenized problem is not a reiterated one.

We prove a global in time existence theorem, for the initial value problem for the Einstein-Boltzmann system, with arbitrarily large initial data, in the homogeneous case, in a Bianchi type I space-time

We prove a global in time existence theorem, for the initial value problem for the Einstein-Boltzmann system, with arbitrarily large initial data, in the homogeneous case, in a Bianchi Type I space-time.

We prove, for the relativistic Boltzmann equation on a Bianchi Type I space-time, a global existence and uniqueness theorem, for arbitrarily large initial data.