arXiv subjects

Saloua Mani Aouadi

Publications and source records attributed to Saloua Mani Aouadi.

2 recordsLinked to original sources

arXiv2022

Analysis of a tumor growth model with a nonlocal boundary condition

In this paper, we conduct a thorough mathematical analysis of a tumor growth model with treatments. The model is a system describing the evolution of metastatic tumors and the number of cells present in a primary tumor. The former evolution is described by a linear transport equation and the latter by an ordinary differential equation of Gompertzian type. The two dynamics are coupled through a nonlocal boundary condition that takes into account the tumor colonization rate. We prove an existence result where the main difficulty is to deal with the coupling and to take into account the time discontinuities generated by treatment terms. We also present numerical tests that highlight the effect of different treatments.

math.AP↗

arXiv2021

Recovering the initial condition in the One-Phase Stefan problem

We consider the problem of recovering the initial condition in the one-dimensional one-phase Stefan problem for the heat equation from the knowledge of the position of the melting point. We first recall some properties of the free boundary solution. Then we study the uniqueness and stability of the inversion. The principal contribution of the paper is a new logarithmic type stability estimate that shows that the inversion may be severely ill-posed. The proof is based on integral equations representation techniques, and the unique continuation property for parabolic type solutions. We also present few numerical examples operating with noisy synthetic data.

math.AP↗