Well-posedness and spectral properties of heat and wave equations with non-local conditions

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:256

Article

Mugnolo, Delio¹  Nicaise, Serge² 

[1] Univ Ulm, Inst Anal, D-89069 Ulm, Germany

[2] Univ Valenciennes & Hainaut Cambresis, LAMAV, FR CNRS 2956, ISTV, F-59313 Valenciennes 9, France

关键词: Non-local conditions;    Analytic semigroups;    Quadratic forms;    Weyl asymptotics;   

DOI  :  10.1016/j.jde.2013.12.016

来源: Elsevier

【 摘 要 】

We consider the one-dimensional heat and wave equations but - instead of boundary conditions - we impose on the solution certain non-local, integral constraints. An appropriate Hilbert setting leads to an integration-by-parts formula in Sobolev spaces of negative order and eventually allows us to use semigroup theory leading to analytic well-posedness, hence sharpening regularity results previously obtained by other authors. In doing so we introduce a parametrization of such integral conditions that includes known cases but also shows the connection with more usual boundary conditions, like periodic ones. In the self-adjoint case, we even obtain eigenvalue asymptotics of so-called Weyl's type. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free