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Generalized lubrification models blow-up and global existence result.

J. Emile Rakotoson, J. Michel Rakotoson, Cédric Verbeke (2005)

RACSAM

We study a general mathematical model linked with various physical models. Especially, we focus on those models established by King or Spencer-Davis-Voorhees related to thin films extending the lubrication model studied by Bernis-Friedman. According to the initial data, we prove that, either, blow up or global existence can be obtained.

Measure-valued solutions of a heterogeneous Cahn-Hilliard system in elastic solids

Irena Pawłow, Wojciech M. Zajączkowski (2008)

Colloquium Mathematicae

The paper is concerned with the existence of measure-valued solutions to the Cahn-Hilliard system coupled with elasticity. The system under consideration is anisotropic and heterogeneous in the sense of admitting the elasticity and gradient energy tensors dependent on the order parameter. Such dependences introduce additional nonlinearities to the model for which the existence of weak solutions is not known so far.

Nonlinear evolution inclusions arising from phase change models

Pierluigi Colli, Pavel Krejčí, Elisabetta Rocca, Jürgen Sprekels (2007)

Czechoslovak Mathematical Journal

The paper is devoted to the analysis of an abstract evolution inclusion with a non-invertible operator, motivated by problems arising in nonlocal phase separation modeling. Existence, uniqueness, and long-time behaviour of the solution to the related Cauchy problem are discussed in detail.

On a Caginalp phase-field system with a logarithmic nonlinearity

Charbel Wehbe (2015)

Applications of Mathematics

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.

On a conserved Penrose-Fife type system

Gianni Gilardi, Andrea Marson (2005)

Applications of Mathematics

We deal with a class of Penrose-Fife type phase field models for phase transitions, where the phase dynamics is ruled by a Cahn-Hilliard type equation. Suitable assumptions on the behaviour of the heat flux as the absolute temperature tends to zero and to + are considered. An existence result is obtained by a double approximation procedure and compactness methods. Moreover, uniqueness and regularity results are proved as well.

On periodic solution of a nonlinear beam equation

Marie Kopáčková (1983)

Aplikace matematiky

the existence of an ω -periodic solution of the equation 2 u t 2 + α 4 u x 4 + γ 5 u x 4 t - γ ˜ 3 u x 2 t + δ u t - β + 0 n u x 2 ( · , ξ ) d ξ + σ 0 n 2 u x t ( · , ξ ) u x ( · , ξ ) d ξ 2 u x 2 = f sarisfying the boundary conditions u ( t , 0 ) = u ( t , π ) = 2 u x 2 t , 0 = 2 u x 2 t , π = 0 is proved for every ω -periodic function f C 0 , ω , L 2 .

On the derivation and mathematical analysis of some quantum–mechanical models accounting for Fokker–Planck type dissipation: Phase space, Schrödinger and hydrodynamic descriptions

José Luis López, Jesús Montejo–Gámez (2013)

Nanoscale Systems: Mathematical Modeling, Theory and Applications

This paper is intended to provide the reader with a review of the authors’ latest results dealing with the modeling of quantum dissipation/diffusion effects at the level of Schrödinger systems, in connection with the corresponding phase space and fluid formulations of such kind of phenomena, especially in what concerns the role of the Fokker–Planck mechanism in the description of open quantum systems and the macroscopic dynamics associated with some viscous hydrodynamic models of Euler and Navier–Stokes...

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