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The aim of this work is to deduce the existence of solution of a coupled problem arising in elastohydrodynamic lubrication. The lubricant pressure and concentration are modelled by Reynolds equation, jointly with the free-boundary Elrod-Adams model in order to take into account cavitation phenomena. The bearing deformation is solution of Koiter model for thin shells. The existence of solution to the variational problem presents some difficulties: the coupled character of the equations, the nonlinear...
The aim of this work is to deduce the existence of solution
of a coupled problem arising in elastohydrodynamic
lubrication. The lubricant pressure and concentration are
modelled by Reynolds equation, jointly with the free-boundary
Elrod-Adams model in order to take into account cavitation
phenomena. The bearing deformation is solution of Koiter
model for thin shells. The existence of solution to the
variational problem presents some difficulties: the coupled
character of the equations, the nonlinear...
In this paper we consider a two-phase one-dimensional free boundary problem for the heat equation, arising from a mathematical model for a Bingham-like fluid with a visco-elastic core. The main feature of this problem consists in the very peculiar structure of the free boundary condition, not allowing to use classical tools to prove well posedness. Existence of classical solution is proved using a fixed point argument based on Schauder's theorem. Uniqueness is proved using a technique based on a...
A mathematical model of the tumour growth along a blood vessel is proposed. The
model employs the mixture theory approach to describe a tissue which consists of cells, extracellular
matrix and liquid. The growing tumour tissue is supposed to be surrounded by the host
tissue. Tumours where complete oxydation of glucose prevails are considered. Special attention is
paid to consistent description of oxygen consumption and growth processes based on the energy
balance. A finite difference numerical...
We consider a free interface problem for the Navier-Stokes equations. We obtain local in time unique existence of solutions to this problem for any initial data and external forces, and global in time unique existence of solutions for sufficiently small initial data. Thanks to global in time maximal regularity of the linearized problem, we can prove a global in time existence and uniqueness theorem by the contraction mapping principle.
The paper is devoted to mathematical modelling and numerical computations of a
nonstationary
free boundary problem. The model is based on processes of molecular diffusion of
some
products of chemical decomposition of a solid organic substance concentrated in
bottom sediments.
It takes into account non-stationary multi-component and multi-stage chemical
decomposition of
organic substances and the processes of sorption desorption under aerobic and
anaerobic conditions.
Such a model allows one to...
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