The main objective of the paper is to state newly fixed point theorems for set-valued mappings in the framework of 0-complete partial metric spaces which speak about a location of a fixed point with respect to an initial value of the set-valued mapping by using some $C$-class functions. The results proved herein generalize, modify and unify some recent results of the existing literature. As an ...

In this work, we study the local wellposedness of solution to a nonlinear elliptic-dispersive coupled system which serves as model for Micro-Electro-Mechanical System (MEMS). A simple electrostatically actuated MEMS capacitor device consists two parallel plates separated by gas-filled thin gap. The modelling combines linear elliptic equation gas pressure with semilinear dispersive gap width. We...

In this paper, applying two theorems of Ricceri and Bonanno, we will establish the existence of three weak solutions for a quasilinear elliptic system. Indeed, we will assign a differentiable nonlinear operator to a differential equation system such that the critical points of this operator are weak solutions of the system. In this paper, applying two theorems of R...

We study the existence of weak solutions to a mixture model for tumour growth that consists of a Cahn–Hilliard–Darcy system coupled with an elliptic reactiondiffusion equation. The Darcy law gives rise to an elliptic equation for the pressure that is coupled to the convective Cahn–Hilliard equation through convective and source terms. Both Dirichlet and Robin boundary conditions are considered ...

Abstract. We consider a nonlinear system of elliptic equations, which arises when modelling the heat diffusion problem coupled with the electrical diffusion problem. The ohmic losses which appear as a source term in the heat diffusion equation yield a nonlinear term which couples both equations. A finite element scheme and a finite volume scheme are considered for the discretization of the syst...

This paper presents some of the results of the simulation in the radiation section of an industrial boiler using an advanced mathematical model. Calculations are described for the flow, heat transfer, and chemical reaction processes occurring within a gas-fired cylindrical furnace. The calculation procedure is a two dimensional one in which the main hydrodynamic variables are the velocity and s...