【摘要】 考虑下面带有齐次Dirichlet边界条件的非局部抛物方程的稳态解及其稳定性,ut=Δu+λf(u)/[∫Ωf(u)dx]p,x∈Ω,t>0,这里λ>0,0<p≤1,f是单调减函数,ΩRn为有界光滑凸区域,证明了上述方程对应稳态解的存在唯一性,并利用稳态解构造出一个随时间递减的上解和随时间递增的下解,从而得到对任意的λ>0,u(x,t)是整体存在的,并且稳态解是全局渐近稳定的.更多还原

【Abstract】 In this paper,we consider the the following nonlocal parabolic equationut=Δu+λf(u)/[∫Ωf(u)dx[p,x∈Ω,t>0 with homogeneous Dirichlet boundary condition,where λ>0,0<p≤1,fis decreasing,ΩRn is a bounded smooth domain.First,we prove that there exists a unique stationary solution corresponding to the above equation.Secondly,we use the stationary solution to construct a lower solution which is increasing with respect to time and an upper solution which is decreasing with respect to time to obtain that u(x,t) is globally bounded and the stationary solution is globally asymptotically stable for any λ>0.更多还原