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Außenraumaufgaben in der linearen Elastizitätstheorie
Author(s) -
Leis R.
Publication year - 1980
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670020402
Subject(s) - mathematics , boundary value problem , resolvent , differential operator , isotropy , essential spectrum , mathematical analysis , spectrum (functional analysis) , operator (biology) , ball (mathematics) , linear map , pure mathematics , physics , biochemistry , chemistry , repressor , quantum mechanics , transcription factor , gene
The paper starts with a short survey of the treatment of initial‐boundary‐value problems in temperature‐free linear elasticity with unisotropic media. The main part of the paper is concerned with exterior initial‐boundary‐value problems in thermoelasticity. In this case the underlying differential operator A is no longer selfadjoint. Thus the spectrum of A has to be discussed. In 2.1 it is shown that all λ with Re λ < 0 belong to the resolvent set. In 2.2 the case G = R 3 with homogeneous isotropic media is considered. Let Λ be the essential spectrum in this case. In 2.3 Λ depending on the thermic coupling parameter is discussed. 2.4 treats the spectrum of A assuming the medium to be homogeneous and isotrop outside a large ball. In this case Λ is the essential spectrum for A too. Radiation conditions are formulated. Finally 2.5 presents a short treatment of the time dependent case with Laplace‐transformation.