Juliana Sartori Ziebell

arXiv2026

A One-Dimensional Integral Equation for a Porous Horizontal Disc under Water Waves

Wave scattering by a thin, porous circular plate submerged in deep water is investigated. The problem is formulated as a second-kind hypersingular Fredholm integral equation over the unit disk, solved numerically using the Boundary Element Method. The analysis focuses on calculating hydrodynamic forces, specifically added mass (real part) and damping coefficient (imaginary part). Results demonstrate the influence of the porosity parameter G: less porous plates (G real) increase added mass and hydrodynamic force, while more porous plates (G imaginary) reduce these effects but increase the damping coefficient. The proposed formulation is validated, showing excellent agreement with established literature.

physics.flu-dyn↗

arXiv2019

Decay Estimates for Solutions of Porous Medium Equations with Advection

In this paper, we show that bounded weak solutions of the Cauchy problem for general degenerate parabolic equations of the form \begin{equation} \notag u_t \,+\; \mbox{div}\,f(x,t,u) \;=\; \mbox{div}\,(\;\!|\,u\,|^α \, \nabla u \;\!), \quad \;\; x \in \mathbb{R}^{n}\!\:\!, \; t > 0, \end{equation} where $ α> 0 \, $ is constant, decrease to zero, under fairly broad conditions on the advection flux $f$. Besides that, we derive a time decay rate for these solutions.

math.AP↗