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This paper is concerned with a multi-dimensional free boundary problemmodeling the growth of a tumor with two species of cells: proliferating cellsand quiescent cells. This free boundary problem has a unique radial stationarysolution. By using the Fourier expansion of functions on unit sphere viaspherical harmonics, we establish some decay estimates for the solution of thelinearized system of this tumor model at the radial stationary solution, sothat proving that the radial stationary solution is linearly asymptoticallystable when neglecting translations.

Linearized stability for a multi-dimensional free boundary problem modeling two-phase tumor growth