In David et al. (Adv Math 350:1109–1192, 2019) and Toro (Regularity of almost minimizers with free boundary. Calculus variations PDEs, 2020), the authors studied for functionals type first by Alt Caffarelli (J Reine Angew 325:105–144, 1981) (Trans Am Soc 282:431–461, 1984). this paper we study regularity to energy variable coefficients (as opposed Caffarelli, J 1981; al., Trans 1984; Adv 2019; ...

the volumetric expansion coefficient has an importance in determination of the free convection heat transfer coefficient. the buoyant force in the fluid which is the result of the variation of fluid density with temperature, is proportional to this expansion coefficient, b. this coefficient of b varies with temperature and it is important to understand under what conditions it should be evaluat...

Krylov subspace spectral (KSS) methods have been demonstrated to be effective tools for solving time-dependent variable-coefficient PDE. They employ techniques developed by Golub and Meurant for computing elements of functions of matrices to approximate each Fourier coefficient of the solution using a Gaussian quadrature rule that is tailored to that coefficient. In this paper, we apply this sa...

In varying coefficient models, three types of variable selection problems are of practical interests: separation of varying and constant effects, selection of variables with nonzero varying effects, and selection of variables with nonzero constant effects. Existing variable selection methods in the literature often focus on only one of the three types. In this paper, we develop a unified variab...

5 Abstract We present a new method in order to get variable slip coefficient in binary lattice Boltzmann models to simulate gaseous flows. Boundary layer theory is presented. We study both the singleand multi-fluid BGK-type models as well. The boundary slip and the Knudsen layer are analyzed in detail. Benchmark simulations are carried out in order to compare the analytical derivation with the ...