The purpose of this course is to study the dynamics of PDE on thin domains. The main
motivation of this kind of problems comes from two sources. The first source is physics; thin …

We summarize the properties of eigenvalues and eigenfunctions of the Laplace operator in
bounded Euclidean domains with Dirichlet, Neumann, or Robin boundary condition. We …

This survey is devoted to an introduction to the theory of global attractors for semigroups
defined on infinite dimensional spaces, which has mainly been developed in the last three …

This paper provides a starting point for researchers and practitioners from biology, medicine,
physics and engineering who can benefit from an up-to-date literature survey on patient …

The present paper seeks to continue the analysis in Barbu et al.[Tangential boundary
stabilization of Navier–Stokes equations, Memoir AMS, to appear] on tangential boundary …

The solution of a PDE over varying initial/boundary conditions on multiple domains is
needed in a wide variety of applications, but it is computationally expensive if the solution is …

We investigate in this paper the existence of a metric which maximizes the first eigenvalue of
the Laplacian on Riemannian surfaces. We first prove that, in a given conformal class, there …

We analyze the dynamics of a reaction–diffusion equation with homogeneous Neumann
boundary conditions in a dumbbell domain. We provide an appropriate functional setting to …

We introduce a new method to triangulate planar, curved domains that transforms a specific
collection of triangles in a background mesh to conform to the boundary. In the process, no …

We present a review of known results in shape optimization from the point of view of
Geometric Analysis. This paper is devoted to the mathematical aspects of the shape …