arXiv subjects

Amah Séna d'Almeida

Publications and source records attributed to Amah Séna d'Almeida.

4 recordsLinked to original sources

arXiv2026

Existence and uniqueness of classical solution to an initial-boundary value problem for the unsteady general planar Broadwell model with four velocities

We consider the unsteady problem for the general planar Broadwell model with four velocities in a rectangular spatial domain over a finite time interval. We impose a class of non-negative initial and Dirichlet boundary data that are bounded and continuous, along with their first-order partial derivatives. We then prove the existence and uniqueness of a non-negative continuous solution, bounded together with its first-order partial derivatives, to the initial-boundary value problem.

math.AP↗

arXiv2026

On the existence and uniqueness of classical solution for an initial-boundary value problem for a discrete Boltzmann system in two space dimensions

The initial-boundary value problem for the two-dimensional regular four-velocity discrete Boltzmann system is analyzed in a rectangle. The existence and uniqueness of a classical global positive solution, bounded with its first partial derivatives are proved for a range of bounded data by the use of fixed points tools. A bound for the solution and its partial derivatives is provided.

math.AP↗

arXiv2026

Global classical solutions for the general planar Broadwell model with arbitrary velocity orientation: a fixed-point framework

The present work extends a fixed-point framework previously developed for the standard planar four-velocity Broadwell model to the general four-velocity configuration with an arbitrary orientation of the discrete velocities. This provides a non-axis-aligned test of the framework and leads to a global-in-time existence and uniqueness result for classical solutions of the associated initial-boundary value problem in a rectangular domain. Under suitable assumptions on the initial and boundary data, we establish the existence and uniqueness of a global-in-time classical solution. The analysis identifies the geometric and analytic properties of the fixed-point approach that remain valid independently of the orientation of the discrete velocities. The results demonstrate the applicability of the framework to the general planar four-velocity Broadwell model beyond the standard axis-aligned configuration.

math.AP↗

arXiv2025

Effective longitudinal wave through a random distribution of poroelastic spheres in a poroelastic matrix

A random distribution of poroelastic spheres in a poroelastic medium obeying Biot's theory is considered. The scattering coefficients of the fast and the slow waves are computed in the low frequency limit using the sealed pore boundary conditions. Analytical expressions of the effective wavenumbers of the coherent longitudinal waves (fast and slow) are deduced the Rayleigh limit using a generalization of the Linton-Martin (LM) formula to poroelastic medium up to the order two in concentration. Some effective quantities (mass density, bulk modulus) of the heterogeneous media are estimated.

cond-mat.soft↗