摘要
In this paper, we study the well-posedness of the third-order differential equation with finite delay(P3): αu’"(t) + u"(t) = Au(t) + Bu’(t) + Fut +f(t)(t ∈ T := [0,2π]) with periodic boundary conditions u(0) = u(2π), u’(0) = u"(2π),u"(0)=u"(2π) in periodic Lebesgue-Bochner spaces Lp(T;X) and periodic Besov spaces Bp,qs(T;X), where A and B are closed linear operators on a Banach space X satisfying D(A) ∩ D(B) ≠ {0}, α≠ 0 is a fixed constant and F is a bounded linear operator from Lp([-2π, 0];X)(resp. Bp,qs([-2π, 0];X)) into X, ut is given by ut(s) = u(t + s) when s ∈ [-2π,0]. Necessary and sufficient conditions for the Lp-well-posedness(resp. Bp,qs-well-posedness)of(P3) are given in the above two function spaces. We also give concrete examples that our abstract results may be applied.
In this paper, we study the well-posedness of the third-order differential equation with finite delay（P3）: αu’"（t） + u"（t） = Au（t） + Bu’（t） + Fut +f（t）（t ∈ T := [0,2π]） with periodic boundary conditions u（0） = u（2π）, u’（0） = u"（2π）,u"（0）=u"（2π） in periodic Lebesgue-Bochner spaces Lp（T;X） and periodic Besov spaces Bp,qs（T;X）, where A and B are closed linear operators on a Banach space X satisfying D（A） ∩ D（B） ≠ {0}, α≠ 0 is a fixed constant and F is a bounded linear operator from Lp（[-2π, 0]; X）（resp. Bp,qs（[-2π, 0]; X）） into X, ut is given by ut（s） = u（t + s） when s ∈ [-2π,0]. Necessary and sufficient conditions for the Lp-well-posedness(resp. Bp,qs-well-posedness)of（P3） are given in the above two function spaces. We also give concrete examples that our abstract results may be applied.
基金
Supported by the NSF of China(Grant Nos.11571194,11731010 and 11771063)
the Natural Science Foundation of Chongqing(Grant No.cstc2017jcyjAX0006)
Science and Technology Project of Chongqing Education Committee(Grant No.KJ1703041)
the University Young Core Teacher Foundation of Chongqing(Grant No.020603011714)
Talent Project of Chongqing Normal University(Grant No.02030307-00024)
