2014/12/04 by Amal Alphonse, Charles M. Elliott, Alphonse, Amal +3
Mathematics · #35K90 #35R01 #35R37 #46E35 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35K90 #msc:35R01 #msc:35R37 #msc:46E35
paper · pdf · doi:10.48550/arxiv.1412.1624
32 pages. Section 3 recalls the main results and notation of our earlier work arXiv:1403.4500
arxiv created 2015/08/02 · arxiv updated 2015/08/04
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.