We study a dynamic model for viscoelastic materials based on a constitutive equation of fractional order. This results in an integrodifferential equation with a weakly singular convolution kernel. We discretize in the spatial variable by a standard Galerkin finite element method. We prove stability and regularity estimates which show how the convolution term introduces dissipation into the equa...

A class of desingularizations for orbit closures of representations of Dynkin quivers is constructed, which can be viewed as a graded analogue of the Springer resolution. A stratification of the singular fibres is introduced; its geometry and combinatorics are studied. Via the Hall algebra approach, these constructions relate to bases of quantized enveloping algebras. Using Ginzburg’s theory of...

A survey of known results in the theory of convolution type Calderón-Zygmund singular integral operators with rough kernels is given. Some recent progress is discussed. A list of remaining open questions is presented.

We consider a fractional order viscoelasticity problem modelled by power-law type stress relaxation function. This viscoelastic is Volterra integral equation of the second kind with weakly singular kernel where convolution corresponds to differentiation/integration. use spatial finite element method and difference scheme in time. Due weak singularity, integration time managed approximately line...