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Regularity and stability for a viscoelastic material with a singular memory kernel

✍ Scribed by G. Gentili

Publisher
Springer Netherlands
Year
1995
Tongue
English
Weight
605 KB
Volume
37
Category
Article
ISSN
0374-3535

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✦ Synopsis

We consider a linear viscoelastic material whose relaxation function may exhibit an initial singularity. We show that the Laplace transform method is still applicable in order to study existence, uniqueness and asymptotic behaviour of the solution to the dynamic problem. In order to provide these results, we impose on the relaxation function only restrictions deriving from Thermodynamics. Moreover, by using energy estimates, we establish a stability theorem. Finally, for a class of singular kernels, we obtain a regularity result which ensures the asymptotic stability of the solution.

πŸ“œ SIMILAR VOLUMES

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## Communicated by B. Brosowski A phase-field model based on the Coleman-Gurtin heat flux law is considered. The resulting system of non-linear parabolic equations, associated with a set of initial and Neumann boundary conditions, is studied. Existence, uniqueness, and regularity results are prove