摘要
We study the well-posedness of the second order degenerate integro-differential equations （P2）： （Mu）t＇（t） ＋ a（Mu）＇（t） = Au（t） ＋ ft_c~ a（t - s）Au（s）ds ＋ f（t）, 0 ≤ t ≤ 27r, with periodic boundary conditions Mu（O） = Mu（27r）, （Mu）＇（O） = （Mu）＇（2π）, in periodic Lebesgue-Bochner spaces LP（T,X）, periodic Besov spaces BBp,q（T, X） and periodic Triebel-Lizorkin spaces F~,q（＇F, X）, where A and M are closed linear operators on a Banach space X satisfying D（A） C D（M）, a C LI（R＋） and a is a scalar number. Using known operator- valued Fourier multiplier theorems, we completely characterize the well-posedness of （P2） in the above three function spaces.
We study the well-posedness of the second order degenerate integro-differential equations(P2):(Mu)(t)+α(Mu)(t) = Au(t)+ft-∞ a(ts)Au(s)ds + f(t),0t2π,with periodic boundary conditions M u(0)=Mu(2π),(Mu)(0) =(M u)(2π),in periodic Lebesgue-Bochner spaces Lp(T,X),periodic Besov spaces B s p,q(T,X) and periodic Triebel-Lizorkin spaces F s p,q(T,X),where A and M are closed linear operators on a Banach space X satisfying D(A) D(M),a∈L1(R+) and α is a scalar number.Using known operatorvalued Fourier multiplier theorems,we completely characterize the well-posedness of(P2) in the above three function spaces.
基金
supported by National Natural Science Foundation of China(Grant No.11171172)
