arXiv subjects

Padi Fuster Aguilera

Publications and source records attributed to Padi Fuster Aguilera.

4 recordsLinked to original sources

arXiv2026

Boundary symmetry breaking via logistic damping in a chemotaxis-growth system

We establish global stability for a chemotaxis-growth model with logarithmic sensitivity under dynamic Dirichlet boundary conditions on a 1D domain. We analyze both parabolic-parabolic and parabolic-hyperbolic systems. The key challenge is handling time-dependent boundary data for the unknown functions. We overcome this by introducing dynamic reference profiles which suitably interpolate boundary values. Using an expanded entropy functional measuring deviation from these profiles, we prove energy estimates the uniform boundedness of solutions and global asymptotic stability of perturbations.

math.AP↗

arXiv2025

Thin shell limit and the derivation of the viscosity operator on the ellipsoid

In this paper we derive four new candidates for an intrinsic viscosity operator on an ellipsoid by using the heuristic of the thin shell limit along the scaling direction of the ellipsoid. We show that the general method of the thin shell limit through the asymptotic expansion depends on the averaging method used. We consider both the homogeneous Navier and Hodge boundary conditions. We also obtain a geometric representation of these two boundary conditions.

math.AP↗

arXiv2023

Global stability of a logarithmically sensitive chemotaxis model under time-dependent boundary conditions

This paper studies the dynamical behavior of classical solutions to a hyperbolic system of balance laws, derived from a chemotaxis model with logarithmic sensitivity, subject to time-dependent boundary conditions. It is shown that under suitable assumptions on the boundary data, solutions starting in $H^2$-space exist globally in time and the differences between the solutions and their corresponding boundary data converge to zero, as time goes to infinity. There is no smallness restriction on the magnitude of initial perturbations. Moreover, numerical simulations show that the assumptions on the boundary data are necessary for the above mentioned results.

math.AP↗

arXiv2020

A PDE model for chemotaxis with logarithmic sensitivity and logistic growth

In this paper, we study the initial-boundary value problem and its asymptotic behavior for a repulsive chemotaxis model with logarithmic sensitivity and logistic growth. We establish global well-posedness of strong solutions for large initial data with Neumann boundary conditions and, moreover, establish the qualitative result that both the population density and chemical concentration asymptotically converge to constant states with the population density specifically converging to its carrying capacity. We additionally prove that the vanishing chemical diffusivity limit holds in this regime. Lastly, we provide numerical confirmation of the rigorous qualitative results, as well as numerical simulations that demonstrate a separation of scales phenomenon.

math.AP↗