Stress obtained by interpolation methods for a boundary value problem in linear viscoelasticity |
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Authors: | W Desch E Fašanga |
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Institution: | a Institut für Mathematik und Wissenschaftliches Rechnen, Karl-Franzens-Universität Graz, Heinrichstrasse 36, A-8010 Graz, Austria b Department of Mathematical Analysis, Charles University, Sokolovská 83, 186 75 Prague, Czech Republic |
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Abstract: | We will solve the following boundary value problem in linear viscoelasticity: given the value of the stress on (a part of) the boundary of the domain find the stress in the whole body at all positive times. Using a state space setting we show that the stress field inside the body can be obtained from the boundary stress by a variation-of-parameters formula involving an analytic semigroup. The relation between the regularities of the boundary stress and the stress inside the body is therefore characterized by the well-known and rich regularity theory for analytic semigroups. |
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