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The stationary Stokes equations for a generalized Newtonian fluid with nonlinear unilateral, and slip and leak boundary conditions are investigated. Boundary conditions include the generalized Clarke gradient and the convex subdifferential, and the variational formulation of the problem is the variational–hemivariational inequality for the velocity field. Existence and uniqueness result for weak solution is proved by using a surjectivity theorem for a pseudomonotone perturbation of a maximal monotone operator. [ABSTRACT FROM AUTHOR]

The aim of this study was to examine the impact of different dietary interventions started at middle age on the metabolic phenotype and gene expression profiling in the hypothalamus. One-year old rats were fed either a control diet, high-fat diet (HFD), HFD supplemented with resveratrol (HFD+RESV), or HFD supplemented with α-ketoglutarate (HFD+AKG). A 6-week HFD feeding led to significant changes in concentrations of plasma glucose, insulin, lipids, and thyroid hormones. Moreover, 32% of the 84 analyzed genes correlated with aging were differentially expressed compared to the control group, with the largest functional class being related to inflammatory response. Dietary RESV ameliorated the changes in plasma glucose, total cholesterol, and triiodothyronine concentrations induced by HFD feeding and significantly downregulated 60% of the surveyed genes compared to the control group, resulting in a major molecular shift compared to HFD alone. In contrast, AKG supplementation did not affect the metabolic phenotype, but prevented the gene expression pattern caused by HFD consumption, mimicking the effects observed in the control group. HFD feeding induces metabolic dysfunction and age-related genetic alterations in the hypothalamus of middle-aged rats, while dietary RESV or AKG may partially retard these effects, even though these compounds act in a different and specific manner. [ABSTRACT FROM AUTHOR]

A generalization of the Oberbeck–Boussinesq model consisting of a system of steady state multivalued partial differential equations for incompressible, generalized Newtonian of thep-power type, viscous flow coupled with the nonlinear heat equation is studied in a bounded domain. The existence of a weak solution is proved by combining the surjectivity method for operator inclusions and a fixed point technique. [ABSTRACT FROM PUBLISHER]

We study a new class of elliptic variational‐hemivariational inequalities in a reflexive Banach space. Based on a surjectivity result for an operator inclusion of Clarke's subdifferential type, we prove existence of solution. Then, we apply this result to a mathematical analysis of the steady Oseen model for a generalized Newtonian incompressible fluid. A variational‐hemivariational inequality for the flow problem is derived and sufficient conditions for existence of weak solutions are obtained. The mixed boundary conditions involve a unilateral boundary condition, the Navier slip condition, a nonmonotone version of the nonlinear Navier‐Fujita slip condition, and the threshold slip and leak condition of frictional type. We study a new class of elliptic variational‐hemivariational inequalities in a reflexive Banach space. Based on a surjectivity result for an operator inclusion of Clarke's subdifferential type, we prove existence of solution. Then, we apply this result to a mathematical analysis of the steady Oseen model for a generalized Newtonian incompressible fluid. A variational‐hemivariational inequality for the flow problem is derived and sufficient conditions for existence of weak solutions are obtained.... [ABSTRACT FROM AUTHOR]