Geodesic
A Stefan problem for a protocell model with symmetry-breaking bifurcations of analytic solutions
Avner Friedman1 ; Bei Hu2 ; Juan José L. Velazques3 orcid
1Ohio State University, Columbus, USA
2University of Notre Dame, USA
3Universidad Complutense de Madrid, Spain
Interfaces and free boundaries, Tome 3 (2001) no. 2, pp. 143-199

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DOI

A simple model of a living cell which undergoes processes of growth and dissolution is described as a free boundary problem for a system of two reaction-diffusion equations; the condition on the free boundary is of the Stefan type. The special case of radially symmetric cells was studied in earlier work. This paper is concerned with the existence of symmetry-breaking stationary solutions, i.e. with solutions which are not radially symmetric. It is proved, in the two-dimensional case, that there exist branches of non-radial stationary solutions bifurcating from radially symmetric solutions; indeed, for any mode l, l [ge] 2, there exists a unique bifurcation branch whose free boundary has the form r = Rl + [epsilon] cos l[theta] + [Sigma]n[ge]2 [epsilon]n[lambda]n ([theta]), | [epsilon] | small, with [lambda]n ([theta]) orthogonal to cos l[theta].
DOI : 10.4171/ifb/37
Classification : 46-XX, 60-XX
Mots-clés : Stefan problem, protocel, bifurcation, symmetry-breaking

Avner Friedman  1   ; Bei Hu  2   ; Juan José L. Velazques  3

1 Ohio State University, Columbus, USA
2 University of Notre Dame, USA
3 Universidad Complutense de Madrid, Spain 
Avner Friedman; Bei Hu; Juan José L. Velazques. A Stefan problem for a protocell model with symmetry-breaking bifurcations of analytic solutions. Interfaces and free boundaries, Tome 3 (2001) no. 2, pp. 143-199. doi: 10.4171/ifb/37
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     title = {A {Stefan} problem for a protocell model with symmetry-breaking bifurcations of analytic solutions},
     journal = {Interfaces and free boundaries},
     pages = {143--199},
     year = {2001},
     volume = {3},
     number = {2},
     doi = {10.4171/ifb/37},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/37/}
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