Zhou, Fujun; Cui, Shangbin Well-posedness and stability of a multidimensional moving boundary problem modeling the growth of tumor cord. (English) Zbl 1147.35121 Discrete Contin. Dyn. Syst. 21, No. 3, 929-943 (2008). Summary: We study a multidimensional moving boundary problem modeling the growth of tumor cord. This problem contains two coupled elliptic equations defined in a bounded domain in \(\mathbb R^2\) whose boundary consists of two disjoint closed curves, one fixed and the other moving and a priori unknown. The evolution of the moving boundary is governed by a Stefan type equation. By using the functional analysis method based on applications of the theory of analytic semigroups, we prove that (1) this problem is locally well-posed in Hölder spaces, (2) it has a unique radially symmetric stationary solution, and (3) this radially symmetric stationary solution is asymptotically stable for arbitrary sufficiently small perturbations in these Hölder spaces. Cited in 8 Documents MSC: 35R35 Free boundary problems for PDEs 35B35 Stability in context of PDEs 76D27 Other free boundary flows; Hele-Shaw flows 76Z05 Physiological flows 92C35 Physiological flow Keywords:moving boundary problem; tumor cord; well-posedness; stability PDFBibTeX XMLCite \textit{F. Zhou} and \textit{S. Cui}, Discrete Contin. Dyn. Syst. 21, No. 3, 929--943 (2008; Zbl 1147.35121) Full Text: DOI