MAXIMAL REGULARITY FOR DEGENERATE DIFFERENTIAL EQUATIONS WITH INFINITE DELAY IN PERIODIC VECTOR-VALUED FUNCTION SPACES

被引：36

作者：

Lizama, Carlos ^{[1
]}

Ponce, Rodrigo ^{[2
]}

机构：

[1] Univ Santiago Chile, Dept Matemat & Ciencia Computac, Santiago, Chile

[2] Univ Talca, Inst Matemat & Fis, Talca, Chile

来源：

PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY | 2013年 / 56卷 / 03期

关键词：

differential equations with delay; operator-valued Fourier multipliers; R-boundedness; UMD spaces; Besov vector-valued spaces; Lebesgue vector-valued spaces; FOURIER MULTIPLIERS; INTEGRODIFFERENTIAL EQUATIONS; BANACH-SPACES; BESOV-SPACES;

D O I：

10.1017/S0013091513000606

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let A and M be closed linear operators defined on a complex Banach space X and let a is an element of L-1(R+) be a scalar kernel. We use operator-valued Fourier multipliers techniques to obtain necessary and sufficient conditions to guarantee the existence and uniqueness of periodic solutions to the equation d/dt (Mu(t)) = Au(t) + integral(t)(-infinity) a(t - s)Au(s)ds + f(t), t > 0, with initial condition Mu(0) = Mu(2 pi), solely in terms of spectral properties of the data. Our results are obtained in the scales of periodic Besov, Triebel-Lizorkin and Lebesgue vector-valued function spaces.

引用

页码：853 / 871

页数：19

共 25 条

[1]

Amann H, 1997, MATH NACHR, V186, P5

[2] On the Strong Solvability of the Navier-Stokes Equations [J].