We present an abstract framework for treating the theory of well-posedness of solutions to
abstract parabolic partial di¤ erential equations on evolving Hilbert spaces. This theory is …

Moving boundary problems are ubiquitous in nature, technology, and engineering.
Examples include the human heart and heart valves interacting with blood flow …

In this paper, we study a new numerical method for the solution of partial differential
equations on evolving surfaces. The numerical method is built on the stabilized trace finite …

We consider a Stokes problem posed on a 2D surface embedded in a 3D domain. The
equations describe an equilibrium, area-preserving tangential flow of a viscous surface fluid …

We develop a unified theory for continuous-in-time finite element discretizations of partial
differential equations posed in evolving domains, including the consideration of equations …

This work addresses an extension of the Aubin–Lions–Simon compactness result to
generalized Bochner spaces L 2 (0, T; H (t)), where H (t) is a family of Hilbert spaces …

In this paper, we propose an approach for solving PDEs on evolving surfaces using a
combination of the trace finite element method and a fast marching method. The numerical …

We develop a functional framework suitable for the treatment of partial differential equations
and variational problems on evolving families of Banach spaces. We propose a definition for …

We consider the Cahn–Hilliard equation with constant mobility and logarithmic potential on
a two-dimensional evolving closed surface embedded in, as well as a related weighted …

We describe a functional framework suitable to the analysis of the Cahn–Hilliard equation
on an evolving surface whose evolution is assumed to be given a priori. The model is …