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We study a variant of the well known Maxwell model for viscoelastic fluids,namely we consider the Maxwell fluid with viscosity and relaxation timedepending on the pressure. Such a model is relevant for example in modellingbehaviour of some polymers and geomaterials. Although it is experimentallyknown that the material moduli of some viscoelastic fluids can depend on thepressure, most of the studies concerning the motion of viscoelastic fluids donot take such effects into account despite their possible practicalsignificance in technological applications. Using a generalized Maxwell modelwith pressure dependent material moduli we solve a simple boundary valueproblem and we demonstrate interesting non-classical features exhibited by themodel.

On Maxwell fluid with relaxation time and viscosity depending on the pressure