初值在L^1中的非局部退化抛物型方程整体解的L~∞估计  

L~∞Estimates of Global Solution for the Non-Local Degenerate Parabolic Equation with Initial Value in L^1

作　　者：石环环[1] 陈才生[1] 徐红梅[1] 

机构地区：[1]河海大学数学系,南京210098

出　　处：《数学学报（中文版）》2011年第3期443-450,共8页Acta Mathematica Sinica：Chinese Series

基　　金：中央高校基本科研业务费资助(B1020268)

摘　　要：考虑非局部退化抛物形方程u_t-div(|▽u|^(m-2)▽u)+k|u|^(μ_u)=|u|^(β-1)u(?)_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u_0∈L^1(Ω)时,整体解u(t)满足估计‖u(t)‖∞≤C(1+t^(-1/μ)),t>0及‖▽u(t)‖∞≤Ct^(-T),0<t≤T,这里k,μ>0,β≥1,α≥0,2<m<N,α+β<μ+1,T是依赖于μ,N,m的正数.We consider the global existence,uniqueness and L~∞estimate of weaksolution to the initial boundary value problem for the nonlocal degenerate parabolicequation u_t—div（｜▽u｜^（m-2）▽u）＋k｜u｜~μu=｜u｜^（β-1）u∫_Ω｜u｜~αdx with zero boundary condition.The following results are established.If u_0∈L^1（Ω）,then the global solutionu（t）exists and satisfies‖u（t）‖_∞≤C（1＋t^（-1/μ））,for t0,and for any T0,‖▽u（t）‖_∞≤Ct^（-（τ））,t∈（0,T）,where k,μ0,β≥1,α≥0,2mN,α＋βμ＋1,τis some positive constant depending onμ,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 

分 类 号：O175.26[理学—数学]