Abstract
This work is devoted to study the limit behavior of weak solutions of an elliptic problem with variable exponent, in a containing structure, of an oscillating nanolayer of thickness and periodicity parameter depending on ε . The generalized Sobolev space is constructed, and the epiconvergence method is considered to find the limit problem with interface conditions.
Highlights
Nanotechnology is the science that deals with matter at the scale of one billionth of a meter and is the study of manipulating matter at the atomic and molecular scale
A mathematical anatomy of the cardiac left ventricle was considered by Koshelev et al in [1], where the ventricle is composed of surfaces that model myocardial layers, each layer is filled with curves corresponding to myocardial fibers
We will be interested to study the minimization problem (5), and the existence of its weak solutions is given in the following proposition
Summary
Nanotechnology is the science that deals with matter at the scale of one billionth of a meter and is the study of manipulating matter at the atomic and molecular scale. Journal of Function Spaces thermal conductivity of nanofluids where potential mechanisms of enhanced heat transport in nanofluids are considered like high heat transport in the nanoparticles, since their thermal conductivity increases in a nonlinear way because most of their atoms are on the surface, and liquid nanolayer at the particle surface, which has a higher thermal conductivity than the liquid itself and so on, see for example [2]. The aim of the present work is to study the problem of existence and limit behavior of a weak solutions for elliptic problem with variable exponent expressed by (1), which presents several mathematical difficulties either in terms of choosing a suitable Luxemburg norm for the considered Sobolev space or using the epiconvergence method to find the limit problem of our model.
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