Almost Periodicity of Parabolic Evolution Equations with Inhomogeneous Boundary Values

被引：6

作者：

Baroun, Mahmoud ^{[1
]}

Maniar, Lahcen ^{[2
]}

Schnaubelt, Roland ^{[3
]}

机构：

[1] Univ Gesamthsch Paderborn, Inst Math, D-33098 Paderborn, Germany

[2] Cadi Ayyad Univ, Fac Sci Semlalia, Marrakech 2390, Morocco

[3] Univ Karlsruhe, Fak Math, Inst Anal, D-76128 Karlsruhe, Germany

来源：

INTEGRAL EQUATIONS AND OPERATOR THEORY | 2009年 / 65卷 / 02期

关键词：

Asymptotic almost periodicity; Fredholm operators; inhomogeneous evolution equation; evolution family; parabolic initial-boundary value problem; inter- and extrapolation; exponential dichotomy; FREDHOLM PROPERTIES; ASYMPTOTIC-BEHAVIOR; CAUCHY-PROBLEMS; OPERATORS; SPACES;

D O I：

10.1007/s00020-009-1704-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show the existence and uniqueness of the (asymptotically) almost periodic solution to parabolic evolution equations with inhomogeneous boundary values on R and R(+/-), if the data are (asymptotically) almost periodic. We assume that the underlying homogeneous problem satisfies the 'Acquistapace-Terreni' conditions and has an exponential dichotomy. If there is an exponential dichotomy only on half intervals (-infinity,-T] and [T,infinity), then we obtain a Fredholm alternative of the equation on R in the space of functions being asymptotically almost periodic on R(+) and R(-).

引用

页码：169 / 193

页数：25

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