Well-posedness of an integro-differential equation with positive type kernels modeling fractional order viscoelasticity

Details Well-posedness of an integro-differential equation with positive type kernels modeling fractional order viscoelasticity Well-posedness of an integro-differential equation with positive type kernels modeling fractional order viscoelasticity

2012-03-18

arxiv.org/abs/1203.4001v1

Mathematics

Numerical Analysis

19 pages

Scientific paper

A hyperbolic type integro-differential equation with two weakly singular kernels is considered together with mixed homogeneous Dirichlet and non-homogeneous Neumann boundary conditions. Existence and uniqueness of the solution is proved by means of Galerkin's method. Regularity estimates are proved and the limitations of the regularity are discussed. The approach presented here is also used to prove regularity of any order for models with smooth kernels, that arise in the theory of linear viscoelasticity, under the appropriate assumptions on data.

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