The Fredholm alternative for parabolic evolution equations with inhornogeneous boundary conditions

被引：9

作者：

Maniar, Lahcen

Schnaubelt, Roland

机构：

[1] Cadi Ayyad Univ, Fac Sci Semlalia, Marrakech, Morocco

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

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2007年 / 235卷 / 01期

关键词：

Fredholm operator; index; exponential dichotomy; inhomogeneous evolution equation; evolution family; parabolic initial-boundary value problem; inter- and extrapolation;

D O I：

10.1016/j.jde.2006.11.018

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the Fredholm properties of parabolic evolution equations on R with inhomogeneous boundary values. These problems are transformed into evolution equations with inhomogeneities taking values in certain extrapolation spaces. Assuming that the underlying homogeneous problem is asymptotically hyperbolic, we show the Fredholm alternative for these equations. The results are applied to parabolic partial differential equations. (c) 2006 Elsevier Inc. All fights reserved.

引用

页码：308 / 339

页数：32

共 36 条

[1] Ordinary differential operators in Hilbert spaces and Fredholm pairs [J].