Time

Oct 22 2008 - 4:30pm - 5:30 pm

Location

MW 154

Speaker

Avner Friedman (OSU)

Abstract

I shall consider a monoclonal tumor with parameters µ, representing the aggressivity of the tumor, and ?, representing the adhesive forces which keep the tumor together. The model equations have a unique stationary spherical solution with radius R; R is independent of µ, ?. This solution will be shown to be asymptotically stable as long as µ/? remains smaller than critical number M_* . It will also be shown that there exists an infinite sequence of symmetry-breaking bifurcation branches of solutions, with free boundary r = R + ?Y_n,0 (?)t.... where Y_n,o (?) is the spherical harmonic of order (n,0); the bifurcation points correspond to values M_n of the parameters µ/?. The parameter M_* is smaller or equal to the smallest of the numbers M_n , and we shall consider the cases where equality (or inequality) holds. Polyclonal tumors will be briefly discussed.