Abstract
In this paper we study eigenvalues of the linearization of a free boundary problem modeling the growth of a tumor containing two species of cells: proliferating cells and quiescent cells. Such eigenvalues are potential bifurcation points from which nonradial solutions of the free boundary problem might bifurcate from the radial solution. A special feature of this problem is that it contains a singular ordinary differential equation which causes the main difficulty of this problem. By using the spherical harmonic expansion method combined with some techniques for solving singular differential integral equations developed in some previous literature, eigenvalues of the linearized problem are completely determined. Invertibility of some linear operators related to the linearized problem in suitable function spaces is also studied which might be useful in the analysis of the original free boundary problem.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
