Blow-up Property Of A Porous Medium System With Nonlocal Boundary Conditions

In this thesis,we mainly consider a porous medium system with nonlocal boundary con-ditions.We prove the global existence and non-global existence of the solutions.In particular, under the conditions of 0＜∫_Ωφ(x,y)dy,int_Ωψ(x,y)dy≤1,we give a precise analysis on the asymptotic behavior of solutions:blow-up.It is interesting to observe that the blow-up exponent is determined by the interaction among the nonlinear diffusion,the reaction and the nonlocal boundary boundary conditions, while the blow-up rate is independent of the nonliear diffusion.The effects from the nonlocal boundary boundary conditions are substatial.