厦门理工学院学报
廈門理工學院學報
하문리공학원학보
Journal of Lujiang University
2015年
5期
84-88
,共5页
双重退化%扩散方程%存在性%唯一性
雙重退化%擴散方程%存在性%唯一性
쌍중퇴화%확산방정%존재성%유일성
doubly degeneracy%diffusion equation%existence%uniqueness
研究带有吸附项双重退化奇异扩散方程??( u)/?t = div( dα?u p-2?u)-uq ,( x,t)∈QT =Ω×(0,T),其中Ω是RN 中边界?Ω充分光滑的有界区域, p >1,α>0,?∈C2, d(x)= dist(x,?Ω)。运用抛物正则化方法验证了当0<α< p -1时,方程存在与初值条件及边值条件有关的唯一解。当α≥p -1时,方程存在仅与初值条件有关且唯一的解。
研究帶有吸附項雙重退化奇異擴散方程??( u)/?t = div( dα?u p-2?u)-uq ,( x,t)∈QT =Ω×(0,T),其中Ω是RN 中邊界?Ω充分光滑的有界區域, p >1,α>0,?∈C2, d(x)= dist(x,?Ω)。運用拋物正則化方法驗證瞭噹0<α< p -1時,方程存在與初值條件及邊值條件有關的唯一解。噹α≥p -1時,方程存在僅與初值條件有關且唯一的解。
연구대유흡부항쌍중퇴화기이확산방정??( u)/?t = div( dα?u p-2?u)-uq ,( x,t)∈QT =Ω×(0,T),기중Ω시RN 중변계?Ω충분광활적유계구역, p >1,α>0,?∈C2, d(x)= dist(x,?Ω)。운용포물정칙화방법험증료당0<α< p -1시,방정존재여초치조건급변치조건유관적유일해。당α≥p -1시,방정존재부여초치조건유관차유일적해。
The doubly degenerate singular diffusion equation with adsorption item ?? u /?t =div dα ?u p -2 ?u -uq x t ∈QT = Ω× 0 T was studied whereΩ?RN as a bounded domain with sufficiently smooth?Ω p > 1 α > 0 ?∈C2 d x = dist x ?Ω . The equation was proved to admit a unique solution subject about given initial data and boundary value condition ifα≥p -1 . While if 0<α<p-1 the equation admits a unique solution only about a given initial value condition.