110,752 research outputs found
Elliptic problems with growth in nonreflexive Orlicz spaces and with measure or data
We investigate solutions to nonlinear elliptic Dirichlet problems of the type
where is a bounded Lipschitz domain in
and is a Carath\'eodory's function. The growth
of~the~monotone vector field with respect to the variables is
expressed through some -functions and . We do not require any
particular type of growth condition of such functions, so we deal with problems
in nonreflexive spaces. When the problem involves measure data and weakly
monotone operator, we prove existence. For -data problems with strongly
monotone operator we infer also uniqueness and regularity of~solutions and
their gradients in the scale of Orlicz-Marcinkiewicz spaces
Finite element approximation of steady flows of generalized Newtonian fluids with concentration-dependent power-law index
We consider a system of nonlinear partial differential equations describing
the motion of an incompressible chemically reacting generalized Newtonian fluid
in three space dimensions. The governing system consists of a steady
convection-diffusion equation for the concentration and a generalized steady
power-law-type fluid flow model for the velocity and the pressure, where the
viscosity depends on both the shear-rate and the concentration through a
concentration-dependent power-law index. The aim of the paper is to perform a
mathematical analysis of a finite element approximation of this model. We
formulate a regularization of the model by introducing an additional term in
the conservation-of-momentum equation and construct a finite element
approximation of the regularized system. We show the convergence of the finite
element method to a weak solution of the regularized model and prove that weak
solutions of the regularized problem converge to a weak solution of the
original problem.Comment: arXiv admin note: text overlap with arXiv:1703.0476
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