## On the bifurcation of the null solutions of some mildly nonlinear elliptic boundary value problems

Abstract Existence and aymptotic expansion of some bifurcated solution for the following boundary value problem: \begin{align*} -\Delta u+cu^{2}-B^{2}u & =0,\ \…

## On the Marangoni and gravity flow in an inclined channel of an arbitrary section

AbstractIn this paper we use a lubrication approximation in order to investigate the flow of a thin layer of a…

## On the Marangoni flow on an inclined plane

AbstractWe consider the flow of a uniform thin layer (rivulet, trickle) of viscous fluid down an inclined plane driven simultaneously…

## FEM and/or BEM for numerical simulation of Marangoni flow

AbstractThe aim of this work is the numerical study of Marangoni effect using three different methods. They are a finite…

## The numerical approximation to positive solution for some reaction-diffusion problems

Abstract A one-dimensional reaction-diffusion problem, with the reaction term of the form $$u^{p}$$, $$p>1$$ is considered. For $$p=3$$, we deduce…

## Surface mobility of surfactant solutions XVI. Involvement of the fluid viscosities in the Marangoni flow – some aspects

AbstractThe influence of viscosity upon the Marangoni flow (induced by surface tension differences) in competition with the gravity flow, through…

## Numerical methods in establishment of concentration profile for the flows with chemical reactions over rotating disk

AbstractA viscous flow due to a rotating disk involving homogeneous as well as heterogeneous chemical reactions is considered. We simplify…

## On the bifurcation and variational approximation of the positive solution of a nonlinear reaction-diffusion problem

Abstract We consider a nonlinear, second-order, two-point boundary value problem that models some reaction-diffusion processes. When the reaction term has…

## On the use of Green’s formula for the solution of the Navier-Stokes equations

AbstractA general iterative procedure for solving Navier-Stokes system in stream function-vorticity variables  is considered. Using the fundamental solution for Laplace…

## On the existence and uniqueness of positive solutions of some mildly nonlinear elliptic boundary value problems

AbstractFor a homogeneous Dirichlet problem attached to a semilinear elliptic equation we study the existence and uniqueness of non-negative solutions.…
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