Scalings in homogenisation of reaction, diffusion and interfacial exchange in a two-phase medium
Segmentation of MRI data by means of nonlinear diffusion
The article focuses on the application of the segmentation algorithm based on the numerical solution of the Allen-Cahn non-linear diffusion partial differential equation. This equation is related to the motion of curves by mean curvature. It exhibits several suitable mathematical properties including stable solution profile. This allows the user to follow accurately the position of the segmentation curve by bringing it quickly to the vicinity of the segmented object and by approaching the details...
Self-propagating high temperature synthesis (SHS) in the high activation energy regime
Shape optimization of turbine blades with the integration of aerodynamics and heat transfer.
Simulation of anisotropic motion by mean curvature -- comparison of phase field and sharp interface approaches.
Simulation of continuously deforming parabolic problems by Galerkin finite-elements method.
Simulation of Indoor Humidity
The paper deals with the moisture in the internal air of a modeling room. The problems connected with the undesired relative humidity of the indoor air are introduced, the reviewing of the hygric situation in the modeling room is described, the less or more precise models for relative humidity estimation depending on the influencing parameters are performed and the reasoning—when, why and how the particular models should be used, is added. As in particular hygric conditions some of the influencing...
Singular limit of a transmission problem for the parabolic phase-field model
A transmission problem describing the thermal interchange between two regions occupied by possibly different fluids, which may present phase transitions, is studied in the framework of the Caginalp-Fix phase field model. Dirichlet (or Neumann) and Cauchy conditions are required. A regular solution is obtained by means of approximation techniques for parabolic systems. Then, an asymptotic study of the problem is carried out as the time relaxation parameter for the phase field tends to 0 in one of...
Solution of temperature distribution in a radiating fin using homotopy perturbation method.
Solution of the basic boundary value problems of stationary thermoelastic oscillations for domains bounded by spherical surfaces.
Solution of the porous media equation by a compact finite difference method.
Solution of the system of differential equations related to Marangoni convections in one fluid layer.
Solvability of a class of phase field systems related to a sliding mode control problem
We consider a phase-field system of Caginalp type perturbed by the presence of an additional maximal monotone nonlinearity. Such a system arises from a recent study of a sliding mode control problem. We prove the existence of strong solutions. Moreover, under further assumptions, we show the continuous dependence on the initial data and the uniqueness of the solution.
Solvability of the inverse problem of finding thermal conductivity.
Solving the axisymmetric inverse heat conduction problem by a wavelet dual least squares method.
Solving the Cahn-Hilliard variational inequality with a semi-smooth Newton method
The Cahn-Hilliard variational inequality is a non-standard parabolic variational inequality of fourth order for which straightforward numerical approaches cannot be applied. We propose a primal-dual active set method which can be interpreted as a semi-smooth Newton method as solution technique for the discretized Cahn-Hilliard variational inequality. A (semi-)implicit Euler discretization is used in time and a piecewise linear finite element discretization of splitting type is used in space leading...
Solving the Cahn-Hilliard variational inequality with a semi-smooth Newton method
The Cahn-Hilliard variational inequality is a non-standard parabolic variational inequality of fourth order for which straightforward numerical approaches cannot be applied. We propose a primal-dual active set method which can be interpreted as a semi-smooth Newton method as solution technique for the discretized Cahn-Hilliard variational inequality. A (semi-)implicit Euler discretization is used in time and a piecewise linear finite element discretization of splitting type is used in space...
Some new results on a Stefan problem in a concentrated capacity
An existence and uniqueness theorem for a nonlinear parabolic system of partial differential equations, connected with the theory of heat conduction with a transition phase in a concentrated capacity, is given in sufficiently general hypotheses on the data.
Some qualitative results for the linear theory of binary mixtures of thermoelastic solids.
In this paper we study the linear thermodynamical problem of mixtures of thermoelastic solids. We use some results of the semigroup theory to obtain an existence theorem for the initial value problem with homogeneous Dirichlet boundary conditions. Continuous dependence of solutions upon the initial data and body forces is also established. We finish with a study of the asymptotic behavior of solutions of the homogeneous problem.
Spatial decay estimates for a class of nonlinear damped hyperbolic equations.