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Displaying 321 –
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901
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...
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...
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...
This note is concerned with proving the finite speed of propagation for some non-local porous medium equation by adapting arguments developed by Caffarelli and Vázquez (2010).
In this paper we deal with a problem of segmentation (including missing boundary completion) and subjective contour creation. For the corresponding models we apply the semi-implicit finite volume numerical schemes leading to methods which are robust, efficient and stable without any restriction to a time step. The finite volume discretization enables to use the spatial adaptivity and thus improve significantly the computational time. The computational results related to image segmentation with partly...
We study the Cauchy problem in the hyperbolic space for the semilinear heat equation with forcing term, which is either of KPP type or of Allen-Cahn type. Propagation and extinction of solutions, asymptotical speed of propagation and asymptotical symmetry of solutions are addressed. With respect to the corresponding problem in the Euclidean space new phenomena arise, which depend on the properties of the diffusion process in . We also investigate a family of travelling wave solutions, named...
Hölder continuity and, basing on this, full regularity and global existence of weak solutions is studied for a general nondiagonal parabolic system of nonlinear differential equations with the matrix of coefficients satisfying special structure conditions and depending on the unknowns. A technique based on estimating a certain function of unknowns is employed to this end.
We consider discontinuous as well as continuous Galerkin methods for the time discretization of a class of nonlinear parabolic equations. We show existence and local uniqueness and derive optimal order optimal regularity a priori error estimates. We establish the results in an abstract Hilbert space setting and apply them to a quasilinear parabolic equation.
We consider discontinuous as well as continuous Galerkin
methods for the time discretization of a class of nonlinear
parabolic equations. We show existence and local uniqueness
and derive optimal order optimal regularity a priori error
estimates. We establish the results in an abstract Hilbert space
setting and apply them to a quasilinear parabolic equation.
Currently displaying 321 –
340 of
901