初值在L1中的非局部退化抛物型方程整体解的L估计

石环环, 陈才生, 徐红梅

数学学报 ›› 2011, Vol. 54 ›› Issue (3) : 443-450.

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PDF(336 KB)
数学学报 ›› 2011, Vol. 54 ›› Issue (3) : 443-450. DOI: 10.12386/A2011sxxb0045
论文

初值在L1中的非局部退化抛物型方程整体解的L估计

    石环环, 陈才生, 徐红梅
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L Estimates of Global Solution for the Non-Local Degenerate Parabolic Equation with Initial Value in L1

    Huan Huan SHI, Cai Sheng CHEN, Hong Mei XU
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摘要

考虑非局部退化抛物形方程ut-div(|▽u|m-2u)+k|u|μu=|u|β-1uΩ|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u0L1(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<tT,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-2u)+k|u|μu=|u|β-1uΩ|u|αdx with zero boundary condition. The following results are established. If u0L1(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

Key words

nonlocal degenerate parabolic equation / existence and uniqueness / L estimates

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导出引用
石环环, 陈才生, 徐红梅. 初值在L1中的非局部退化抛物型方程整体解的L估计. 数学学报, 2011, 54(3): 443-450 https://doi.org/10.12386/A2011sxxb0045
Huan Huan SHI, Cai Sheng CHEN, Hong Mei XU. L Estimates of Global Solution for the Non-Local Degenerate Parabolic Equation with Initial Value in L1. Acta Mathematica Sinica, Chinese Series, 2011, 54(3): 443-450 https://doi.org/10.12386/A2011sxxb0045

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基金

中央高校基本科研业务费资助(B1020268)

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