On some linear parabolic PDEs on moving hypersurfaces

  • Amal Alphonse

    University of Warwick, Coventry, UK
  • Charles M. Elliott

    University of Warwick, Coventry, UK
  • Björn Stinner

    University of Warwick, Coventry, United Kingdom


We consider existence and uniqueness for several examples of linear parabolic equations formulated on moving hypersurfaces. Specifically, we study in turn a surface heat equation, an equation posed on a bulk domain, a novel coupled bulk-surface system and an equation with a dynamic boundary condition. In order to prove the well-posedness, we make use of an abstract framework presented in a recent work by the authors which dealt with the formulation and well-posedness of linear parabolic equations on arbitrary evolving Hilbert spaces. Here, after recalling all of the necessary concepts and theorems, we show that the abstract framework can applied to the case of evolving (or moving) hypersurfaces, and then we demonstrate the utility of the framework to the aforementioned problems.

Cite this article

Amal Alphonse, Charles M. Elliott, Björn Stinner, On some linear parabolic PDEs on moving hypersurfaces. Interfaces Free Bound. 17 (2015), no. 2, pp. 157–187

DOI 10.4171/IFB/338