A degenerate parabolic equation with a nonlocal source and an absorption term

作者：Han Yuzhu^*; Gao Wenjie

来源：Applicable Analysis, 2010, 89(12): 1917-1930.

DOI：10.1080/00036811.2010.505190

• nonlocal source
• absorption term
• blow-up
• global blow-up
• blow-up rate

This article deals with a class of nonlocal and degenerate quasilinear parabolic equation u(t)=f(u)(Delta u + a integral (Omega)u(x, t)dx - u) with homogeneous Dirichlet boundary conditions. The local existence of positive classical solutions is proved by using the method of regularization. The global existence of positive solutions and blow-up criteria are also obtained. Furthermore, it is shown that, under certain conditions, the solutions have global blow-up property. When f(s)=s(p), 0<p <= 1, the blow-up rate estimates are also obtained.

• 单位
  吉林大学