For an elliptic equation with the p(x)-Laplacian, where exponent p(∙) is a bounded measurable function, we find conditions guaranteeing continuity of solution at point.

The symmetry present in Green's functions is exploited to signi®cantly reduce the matrix assembly time for a Galerkin boundary integral analysis. A relatively simple modi®cation of the standard Galerkin implementation for computing the non-singular integrals yields a 20±30 per cent decrease in computation time. This faster Galerkin method is developed for both singular and hypersingular equatio...

This survey is devoted to some fractional extensions of the incomplete lumped formulation, the lumped formulation and the formulation of Lauwerier of the temperature field problem in oil strata. The method of integral transforms is used to solve the corresponding boundary value problems for the fractional heat equation. By using Caputo’s differintegration operator and the Laplace transform, new...

We investigate water infiltration pressure for hydrophobic nanochannels through molecular dynamics simulations. It is found that the entrance energy barrier significantly raises the infiltration pressure, which makes the classic Young-Laplace equation invalid for nanochannels. As the channel surface is tuned from superhydrophobic to hydrophobic, the infiltration pressure is greatly reduced main...