The Fredholm alternative for parabolic evolution equations with inhornogeneous boundary conditions

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:235

Article

Maniar, Lahcen ; Schnaubelt, Roland

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

DOI  :  10.1016/j.jde.2006.11.018

来源: Elsevier

【 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.

【 授权许可】

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