A class of inverse problems for viscoelastic material with dominating Newtonian viscosity

Authors:
Jaan Janno and Lothar von Wolfersdorf

Journal:
Quart. Appl. Math. **57** (1999), 465-474

MSC:
Primary 35R30; Secondary 35Q72, 45K05, 45Q05, 74D05, 76A10

DOI:
https://doi.org/10.1090/qam/1704447

MathSciNet review:
MR1704447

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Abstract | References | Similar Articles | Additional Information

Abstract: Memory kernels in linear stress-strain relations involving a Newtonian viscosity are identified by solving a class of inverse problems. The inverse problems are reduced to nonlinear Volterra integral equations of the first kind which in turn lead to corresponding Volterra equations of the second kind by differentiation. Applying the contraction principle with weighted norms we derive global (in time) existence, uniqueness and stability of the solution to the inverse problems under similar assumptions as for related inverse problems in heat flow.

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DOI:
https://doi.org/10.1090/qam/1704447

Article copyright:
© Copyright 1999
American Mathematical Society