We consider a free boundary problem for a system of partial differential equations, which arises in a model of tumor growth with a necrotic core. For any positive numbers ρ<R, there exists a radially symmetric stationary solution with tumor boundary r = R and necrotic core boundary r=ρ. The system depends on a positive parameter μ, which describes the tumor aggressiveness. There also exists a sequence of values μ 2< μ3<⋯ for which branches of symmetry-breaking stationary solutions bifurcate from the radially symmetric solution branch.
All Science Journal Classification (ASJC) codes
- Economics, Econometrics and Finance(all)
- Computational Mathematics
- Applied Mathematics