Noureddine Igbida

A degenerate elliptic-parabolic problem with nonlinear dynamical boundary conditions

We prove existence and uniqueness of weak solutions for a general degenerate elliptic-parabolic problem with nonlinear dynamical boundary conditions. Particular instances of this problem appear in various phenomena with changes of phase like the multiphase Stefan problem and in the weak formulation of the mathematical model of the so called Hele–Shaw problem. Also, the problem with nonhomogeneous Neumann boundary conditions is included.

Optimal mass transportation for costs given by Finsler distances via p-Laplacian approximations

Abstract In this paper we approximate a Kantorovich potential and a transport density for the mass transport problem of two measures (with the transport cost given by a Finsler distance), by taking limits, as p goes to infinity, to a family of variational problems of p-Laplacian type. We characterize the Euler–Lagrange equation associated to the variational Kantorovich problem. We also obtain different characterizations of the Kantorovich potentials and a Benamou–Brenier formula for the transport problem.

Elliptic-Parabolic Equation with Absorption of Obstacle type

Abstract This paper is concerned with existence and uniqueness of solutions for a doubly nonlinear degenerate parabolic problem of the type β(w)t − div a(x, Dw) + ∂ j ( ., β(w) ) ∋ f, where α is a Leray-Lions operator, β is a nondecreasing continuous function and ∂ j(., r) is a maximal monotone graph with respect to r defined on a closed interval of ℝ. Particular cases of j correspond to the so called obstacle problem.