Abstract

The problem of one-dimensional non-stationary wave propagation in viscoelastic half space is studied. For the description of the hereditary properties of the viscoelastic medium, several examples of completely monotone relaxation kernels are considered. They are expressed in terms of functions of Mittag-Leffler type, including the recently introduced multinomial Prabhakar type function. Applying Laplace transform in time, some characteristics of the propagation function are discussed, such as non-negativity, monotonicity, propagation speed, presence/absence of wave front, and explicit integral representation of the solution is derived.

Citation details of the article

Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 34
Issue: 3
Year: 2021

DOI: 10.12732/ijam.v34i3.1

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