【摘要】 本文研究一类三阶拟线性发展方程ｕｔｔ－Δｕｔ＋ｕｔ＝ｎｉ＝１ｘｉσｉ（ｕｘｉ），（ｘ，ｔ）∈Ω×（０，Ｔ）的初边值问题，其中ΩＲｎ（ｎ≥１）为一有界域．证明了只要σｉ（ｓ）∈Ｃ１，σ′ｉ（ｓ）（ｉ＝１，…，ｎ）有界并且初始函数满足一定的条件，则上述问题存在唯一的整体弱解．更多还原

【Abstract】 The initial boundary value problem for a class of three order quasilinear evolution equationsu ttt -Δu t+u tt =ni=1οοx iσ i(u x i ),,(x,t)∈Ω×(0,T)are studied,where Ω is a bounded domain in R n(n≥1) .It is proved that there exists a unique global weak solution for the above mentioned problem as long as σ i(s)∈C 1,σ′ i (s)(i=1,…,n) are bounded and the initial data satisfy certain conditions.更多还原