Robin边界条件下一类积分偏微分方程的解

THE SOLUTION FOR A CLASS OF INTEGRAL PARTIAL DIFFERENTIAL EQUATIONS IN ROBIN BOUNDARY CONDITION

讨论下列初边值问题２ｕｔ２－ａ２２ｕｘ２＋ａ２∫ｔｏλ（ｔ－ｓ）２ｕｘ２ｄｓ＝ｆ（ｘ，ｔ，ｕ，ｕｔ）ｕｘ（０，ｔ）＋σｕ（０，ｔ）＝０，ｕｘ（Ｌ，ｔ）＋σｕ（Ｌ，ｔ）＝０，ｔ＞０ｕ（ｘ，０）＝φ（ｘ），ｕｔ（ｘ，０）＝ψ（ｘ），０≤ｘ≤Ｌ在一定条件下，证明了该问题强解的整体存在性，唯一性和稳定性。

The global strong solution of the following problem was studied〖JB({) 2ut 2-a 2 2ux 2+a 2∫ t oλ(t-s) 2ux 2ds=f(x,t,u,ut) ux(0,t)+σu(0,t)=0,,ux(L,t)+σu(L,t)=0,t>0 u(x,0)=φ(x),ut(x,0)=ψ(x),,,0≤x≤Lunder certain conditions on λ and f, the unique existence and stability of the global strong solution of this problem were obtained.