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.
Classification :
35-XX, 46-XX
Mots-clés :
Parabolic equations on moving domains; advection-diffusion on evolving surfaces
Affiliations des auteurs :
Amal Alphonse
1
;
Charles M. Elliott
1
;
Björn Stinner
2
1
University of Warwick, Coventry, UK
2
University of Warwick, Coventry, United Kingdom
Amal Alphonse; Charles M. Elliott; Björn Stinner. On some linear parabolic PDEs on moving hypersurfaces. Interfaces and free boundaries, Tome 17 (2015) no. 2, pp. 157-187. doi: 10.4171/ifb/338
@article{10_4171_ifb_338,
author = {Amal Alphonse and Charles M. Elliott and Bj\"orn Stinner},
title = {On some linear parabolic {PDEs} on moving hypersurfaces},
journal = {Interfaces and free boundaries},
pages = {157--187},
year = {2015},
volume = {17},
number = {2},
doi = {10.4171/ifb/338},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/338/}
}
TY - JOUR
AU - Amal Alphonse
AU - Charles M. Elliott
AU - Björn Stinner
TI - On some linear parabolic PDEs on moving hypersurfaces
JO - Interfaces and free boundaries
PY - 2015
SP - 157
EP - 187
VL - 17
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.4171/ifb/338/
DO - 10.4171/ifb/338
ID - 10_4171_ifb_338
ER -
%0 Journal Article
%A Amal Alphonse
%A Charles M. Elliott
%A Björn Stinner
%T On some linear parabolic PDEs on moving hypersurfaces
%J Interfaces and free boundaries
%D 2015
%P 157-187
%V 17
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4171/ifb/338/
%R 10.4171/ifb/338
%F 10_4171_ifb_338
