We consider a phase field system based on the Maxwell Cattaneo heat conduction law, with a logarithmic nonlinearity, associated with Dirichlet boundary conditions. In particular, we prove, in one and two space dimensions, the existence of a solution which is strictly separated from the singularities of the nonlinear term and that the problem possesses a finite-dimensional global attractor in terms of exponential attractors.
The existence of a weak solution of a non-stationary free boundary transmission problem arising in the production of industrial materials is established. The process is governed by a coupled system involving the Navier--Stokes equations and a non-linear heat equation. The stationary case was studied in [7].
We deal with a Penrose-Fife type model for phase transition. We assume a rather general constitutive low for the heat flux and treat the Dirichlet and Neumann boundary condition for the temperature. Some of our proofs apply to different types of boundary conditions as well and improve some results existing in the literature.
The vibration problem in two variables is derived from the spatial situation (a plate as a three-dimensional body) on the basis of geometrically nonlinear plate theory (using Kármán's hypothesis) and coupled linear thermoelasticity. That leads to coupled strongly nonlinear two-dimensional equilibrium and heat conducting equations (under classical mechanical and thermal boundary conditions). For the generalized problem with subgradient conditions on the boundary and in the domain (including also...
We consider the full Navier-Stokes-Fourier system of equations on an unbounded domain with prescribed nonvanishing boundary conditions for the density and temperature at infinity. The topic of this article continues author’s previous works on existence of the Navier-Stokes-Fourier system on nonsmooth domains. The procedure deeply relies on the techniques developed by Feireisl and others in the series of works on compressible, viscous and heat conducting fluids.
The continuity and boundedness of the stress to the solution of the thermoelastic system is studied first for the linear case on a strip and then for the twodimensional model involving nonlinearities, noncontinuous heating regimes and isolated boundary nonsmoothnesses of the heated body.
A quasilinear noncoupled thermoelastic system is studied both on a threedimensional bounded domain with a smooth boundary and for a generalized model involving the influence of supports. Sufficient conditions are derived under which the stresses are bounded and continuous on the closure of the domain.
A short survey of available existence results for dynamic contact problems including heat generation and heat transfer is presented.