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Degenerate triply nonlinear problems with nonhomogeneous boundary conditions

Kaouther Ammar (2010)

Open Mathematics

The paper addresses the existence and uniqueness of entropy solutions for the degenerate triply nonlinear problem: b(v)t − div α(v, ▽g(v)) = f on Q:= (0, T) × Ω with the initial condition b(v(0, ·)) = b(v 0) on Ω and the nonhomogeneous boundary condition “v = u” on some part of the boundary (0, T) × ∂Ω”. The function g is continuous locally Lipschitz continuous and has a flat region [A 1, A 2,] with A 1 ≤ 0 ≤ A 2 so that the problem is of parabolic-hyperbolic type.

Degenerating Cahn-Hilliard systems coupled with mechanical effects and complete damage processes

Christian Heinemann, Christiane Kraus (2014)

Mathematica Bohemica

This paper addresses analytical investigations of degenerating PDE systems for phase separation and damage processes considered on nonsmooth time-dependent domains with mixed boundary conditions for the displacement field. The evolution of the system is described by a degenerating Cahn-Hilliard equation for the concentration, a doubly nonlinear differential inclusion for the damage variable and a quasi-static balance equation for the displacement field. The analysis is performed on a time-dependent...

Discrete anisotropic curvature flow of graphs

Klaus Deckelnick, Gerhard Dziuk (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The evolution of n–dimensional graphs under a weighted curvature flow is approximated by linear finite elements. We obtain optimal error bounds for the normals and the normal velocities of the surfaces in natural norms. Furthermore we prove a global existence result for the continuous problem and present some examples of computed surfaces.

Dislocation dynamics - analytical description of the interaction force between dipolar loops

Vojtěch Minárik, Jan Kratochvíl (2007)

Kybernetika

The interaction between dislocation dipolar loops plays an important role in the computation of the dislocation dynamics. The analytical form of the interaction force between two loops derived in the present paper from Kroupa’s formula of the stress field generated by a single dipolar loop allows for faster computation.

Estimates of the derivatives for a class of parabolic degenerate operators with unbounded coefficients in ℝ N

Luca Lorenzi (2005)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We consider a class of perturbations of the degenerate Ornstein-Uhlenbeck operator in ℝ N . Using a revised version of Bernstein’s method we provide several uniform estimates for the semigroup { T ( t ) } t ≥ 0 associated with the realization of the operator 𝒜 in the space of all the bounded and continuous functions in ℝ N

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