Free Boundary Problem Modeling Growth Of Vascularized Tumor With Inhibition

In this thesis,we study the free boundary problem of partial differential equationes modeling the growth of vascularized tumor with inhibitors.The full text is divided into two parts.In the first part,we introduce the well-known results related on the problem we considered and our main results.In the second part,we discuss the free boundary problem of partial differential equationes modeling vascularized tumor growth with inhibitors:c1σt=Δrσ-λ1σ-β,0<r<R(t),t>0,c2βt=Δrβ-λ2β,0<r<R(t),t>0,(?)+α1(σ-σ)=0,r=R(t),t>0,(?)+α2(β-β)=0,r=R(t),t>0,(?)[σ(r,t)-σ-vβ(r,t)]r2dr,t>0,σ(r,0)=σ0(r),β(r,0)=β0(r),0≤r≤R0,R(0)=R0.Where Δ.=1/r2(?)(r2(?)),σ,β are the concentrations of nutrition and inhibitor concentration in the tumor,R(t)is the free boundary of tumor,(?) is the boundary of the unit normal vector,σ,β are tumor exter-nal nutrient concentrations and inhibitor concentration,α1,α2 are supply rates of nutrient and inhibitor,respectively,where c1,c2,λ1,2,v,μ.are constants,σ0(r),β0(r)∈ C2(0,R0).The quasi-steady state problem(c1=0,c2=0)is discussed first,we prove the existence and unique-ness of the solution of the quasi-stable state problem.By rigorous analysis,it is proved that under certain conditions,limR(t)= 0,namely,the tumor is contracted.Moreover,we study the asymptotic behavior by using the iterative technique.It is concluded that under certain conditions,the solution of the tumor model will converge to the steady-state solution.