Linearized stability for a multi-dimensional free boundary problem modelling two-phase tumour growth.

This paper is concerned with a multi-dimensional free boundary problem modelling the growth of a tumour with two species of cells: proliferating cells and quiescent cells. This free boundary problem has a unique radial stationary solution. By using the Fourier expansion of functions on unit sphere via spherical harmonics, we establish some decay estimates for the solution of the linearized system of this tumour model at the radial stationary solution, so proving that the radial stationary solution is linearly asymptotically stable when neglecting translations. [ABSTRACT FROM AUTHOR]