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Optimal Poiseuille flow in a finite elastic dyadic tree

Benjamin Mauroy, Nicolas Meunier (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper we construct a model to describe some aspects of the deformation of the central region of the human lung considered as a continuous elastically deformable medium. To achieve this purpose, we study the interaction between the pipes composing the tree and the fluid that goes through it. We use a stationary model to determine the deformed radius of each branch. Then, we solve a constrained minimization problem, so as to minimize the viscous (dissipated) energy in the tree. The key...

Optimal potentials for Schrödinger operators

Giuseppe Buttazzo, Augusto Gerolin, Berardo Ruffini, Bozhidar Velichkov (2014)

Journal de l’École polytechnique — Mathématiques

We consider the Schrödinger operator - Δ + V ( x ) on H 0 1 ( Ω ) , where Ω is a given domain of ℝ d . Our goal is to study some optimization problems where an optimal potential V ≥ 0 has to be determined in some suitable admissible classes and for some suitable optimization criteria, like the energy or the Dirichlet eigenvalues.

Optimal Proliferation Rate in a Cell Division Model

P. Michel (2010)

Mathematical Modelling of Natural Phenomena

We consider a size structured cell population model where a mother cell gives birth to two daughter cells. We know that the asymptotic behavior of the density of cells is given by the solution to an eigenproblem. The eigenvector gives the asymptotic shape and the eigenvalue gives the exponential growth rate and so the Maltusian parameter. The Maltusian parameter depends on the division rule for the mother cell, i.e., symmetric (the two daughter cells have the same size) or asymmetric. We use a...

Optimal regularity for one-dimensional porous medium flow.

Donald G. Aronson, Luis A. Caffarelli (1986)

Revista Matemática Iberoamericana

We give a new proof of the Lipschitz continuity with respect to t of the pressure in a one dimensional porous medium flow. As is shown by the Barenblatt solution, this is the optimal t-regularity for the pressure. Our proof is based on the existence and properties of a certain selfsimilar solution.

Optimal regularity for the pseudo infinity Laplacian

Julio D. Rossi, Mariel Saez (2007)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we find the optimal regularity for viscosity solutions of the pseudo infinity Laplacian. We prove that the solutions are locally Lipschitz and show an example that proves that this result is optimal. We also show existence and uniqueness for the Dirichlet problem.

Optimal Screening in Structured SIR Epidemics

B. Ainseba, M. Iannelli (2012)

Mathematical Modelling of Natural Phenomena

We present a model for describing the spread of an infectious disease with public screening measures to control the spread. We want to address the problem of determining an optimal screening strategy for a disease characterized by appreciable duration of the infectiveness period and by variability of the transmission risk. The specific disease we have in mind is the HIV infection. However the model will apply to a disease for which class-age structure...

Optimal time and space regularity for solutions of degenerate differential equations

Alberto Favaron (2009)

Open Mathematics

We derive optimal regularity, in both time and space, for solutions of the Cauchy problem related to a degenerate differential equation in a Banach space X. Our results exhibit a sort of prevalence for space regularity, in the sense that the higher is the order of regularity with respect to space, the lower is the corresponding order of regularity with respect to time.

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