Parabolic equations in time dependent domains

We show existence and uniqueness results for nonlinear parabolic equations in noncylindrical domains with possible jumps in the time variableComment: 22 pages. The uniqueness part was redone. Some minor details have been correcte

On the wave equation on moving domains: regularity, energy balance and application to dynamic debonding

We revisit some issues about existence and regularity for the wave equation in noncylindrical domains. Using a method of diffeomorphisms, we show how, through increasing regularity assumptions, the existence of weak solutions, their improved regularity and an energy balance can be derived. As an application, we give a rigorous definition of dynamic energy release rate density for some problems of debonding, and we formulate a proper notion of solution for such problems. We discuss the consistence of such formulation with previous ones, given in literature for particular cases.Comment: 36 page

Non-stationary incompressible linear fluid equations in a moving domain

This article considers non-stationary incompressible linear fluid equations in a moving domain. We demonstrate the existence and uniqueness of an appropriate weak formulation of the problem by making use of the theory of time-dependent Bochner spaces. It is not possible to directly apply established evolving Hilbert space theory due to the incompressibility constraint. After we have established the well-posedness, we derive and analyse a time discretisation of the system

An evolving space framework for Oseen equations on a moving domain

This article considers non-stationary incompressible linear fluid equations in a moving domain. We demonstrate the existence and uniqueness of an appropriate weak formulation of the problem by making use of the theory of time-dependent Bochner spaces. It is not possible to directly apply established evolving Hilbert space theory due to the incompressibility constraint. After we have established the well-posedness, we derive and analyse a first order time discretisation of the system