Year: 2025
Type: preprint
Abstract: Many mathematical models in different disciplines involve the formulation of free boundary problems, where the domain boundaries are not predefined. These models present unique challenges, notably the nonlinear coupling between the solution and the boundary, which complicates the identification of bifurcation types. This paper mainly investigates the structure of symmetry-breaking bifurcations in a two-dimensional free boundary problem modeling tumor growth. By expanding the solution to a high order with respect to a small parameter and computing the bifurcation direction at each bifurcation point, we demonstrate that all the symmetry-breaking bifurcations occurred in the model, as established by the Crandall-Rabinowitz Bifurcation From Simple Eigenvalue Theorem, are pitchfork bifurcations. These findings reveal distinct behaviors between the two-dimensional and three-dimensional cases of the same model.
Source: arXiv (Cornell University)
Authors: Zhao, Xinyue Evelyn, Shi, Junping
Language: English
Subfield: Modeling and Simulation
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6979350168
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