Exponential attractors for a nonclassical diffusion equation.
Exponential convergence for a periodically driven semilinear heat equation
Exponential decay of a solution for some parabolic equation involving a time nonlocal term
We consider the large time behavior of a solution of a parabolic type equation involving a nonlocal term depending on the unknown function. This equation is proposed as a mathematical model of carbon dioxide transport in concrete carbonation process, and we proved the existence, uniqueness and large time behavior of a solution of this model. In this paper, we derive the exponential decay estimate of the solution of this model under restricted boundary data and initial data.
Extended dynamical systems.
Extension of a result of Ladyženskaja and Uralceva concerning second-order parabolic equations of arbitrary order
Extinction and decay estimates of solutions for a class of porous medium equations.
Extinction for fast diffusion equations with nonlinear sources.
Extremal equilibria for parabolic non-linear reaction-diffusion equations
Extremal Solutions for Nonlinear Parabolic Problems with Discontinuities.
Fattening on two dimensions obtained with a nonsymmetric anisotropy: Numerical simulations.
Feedback stabilization of semilinear heat equations.
Fehlerschranken und Eindeutigkeitsaussagen für die Lösungen nichtlinearer, stark gekoppelter, parabolischer Differentialgleichungssysteme.
Fieldless methods for the simulation of stationary and nonstationary induction heating
Finite difference approximation to the Cauchy problem for non-linear parabolic differential equations
Finite difference scheme for the Willmore flow of graphs
In this article we discuss numerical scheme for the approximation of the Willmore flow of graphs. The scheme is based on the finite difference method. We improve the scheme we presented in Oberhuber [Obe-2005-2,Obe-2005-1] which is based on combination of the forward and the backward finite differences. The new scheme approximates the Willmore flow by the central differences and as a result it better preserves symmetry of the solution. Since it requires higher regularity of the solution, additional...
Finite dimensional dynamics for Kolmogorov-Petrovsky-Piskunov equation.
Finite dimensional global attractor for a class of doubly nonlinear parabolic equations
Our aim in this paper is to study the long time behavior of a class of doubly nonlinear parabolic equations. In particular, we prove the existence of the global attractor which has, in one and two space dimensions, finite fractal dimension.
Finite element approximation of a Stefan problem with degenerate Joule heating
We consider a fully practical finite element approximation of the following degenerate systemsubject to an initial condition on the temperature, , and boundary conditions on both and the electric potential, . In the above is the enthalpy incorporating the latent heat of melting, is the temperature dependent heat conductivity, and is the electrical conductivity. The latter is zero in the frozen zone, , which gives rise to the degeneracy in this Stefan system. In addition to showing stability...
Finite element approximation of a Stefan problem with degenerate Joule heating
We consider a fully practical finite element approximation of the following degenerate system subject to an initial condition on the temperature, u, and boundary conditions on both u and the electric potential, ϕ. In the above p(u) is the enthalpy incorporating the latent heat of melting, α(u) > 0 is the temperature dependent heat conductivity, and σ(u) > 0 is the electrical conductivity. The latter is zero in the frozen zone, u ≤ 0, which gives rise to the degeneracy in this Stefan...
Finite element approximation of a two-layered liquid film in the presence of insoluble surfactants
We consider a system of degenerate parabolic equations modelling a thin film, consisting of two layers of immiscible Newtonian liquids, on a solid horizontal substrate. In addition, the model includes the presence of insoluble surfactants on both the free liquid-liquid and liquid-air interfaces, and the presence of both attractive and repulsive van der Waals forces in terms of the heights of the two layers. We show that this system formally satisfies a Lyapunov structure, and a second energy...