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Bifurcation for a free boundary problem modeling a protocell

โœ Scribed by Hua Zhang; Changzheng Qu; Bei Hu

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
858 KB
Volume
70
Category
Article
ISSN
0362-546X

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โœฆ Synopsis

In this paper we consider a free boundary problem for a physico-chemical model of a protocell. This model of a self-maintaining unity or a protocell is based on the reaction and diffusion process, and a mechanism of self-control of the boundary. For any positive radius R, there exists a radially symmetric solution with radius r = R. In the more realistic threespace-dimensional case, we give a proof that there exist symmetry-breaking bifurcation branches of solutions with free boundary r = R + Y n,0 (ฮธ) + O( 2 ) (n โ‰ฅ 2, even) for small | |, where Y n,0 is the spherical harmonic of mode (n, 0).

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