Huan Huan SHI, Cai Sheng CHEN, Hong Mei XU
We consider the global existence, uniqueness and L∞ estimate of weak solution to the initial boundary value problem for the nonlocal degenerate parabolic equation ut-div(|▽u|m-2▽u)+k|u|μu=|u|β-1u∫Ω|u|αdx with zero boundary condition. The following results are established. If u0∈L1(Ω), then the global solution u(t) exists and satisfies ‖u(t)‖∞≤C(1+t-1/μ), t>0, and for any T > 0, ‖▽u(t)‖∞≤Ct-τ, t ∈ (0, T), where k, μ > 0, β ≥ 1, α ≥ 0, 2 < m< N, α+β < μ+1, τ is some positive constant depending on μ, N, m.