考虑非局部退化抛物形方程ut-div(|▽u|m-2▽u)+k|u|μu=|u|β-1u∫Ω|u|αdx带有零边界条件的初边值问题整体解 u(t) 的存在性、唯一性和 u(t), ▽u(t) 的L∞估计,证明了当u0∈L1(Ω)时,整体解u(t)满足估计‖u(t)‖∞≤C(1+t-1/μ), t>0及‖▽u(t)‖∞≤Ct-τ, 0<t≤T,这里k,μ>0, β≥1, α≥0, 2<m<N, α+β<μ+1, τ是依赖于μ, N, m的正数.
Abstract
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.
关键词
非局部退化抛物型方程 /
存在性和唯一性 /
L∞估计
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Key words
nonlocal degenerate parabolic equation /
existence and uniqueness /
L∞ estimates
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参考文献
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脚注
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