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On the origin of tiger bush
We propose a model which describes the dynamics of vast classes of terrestrial plant communities growing in arid or semi-arid regions throughout the...
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Interfacial phenomenon for one-dimensional equation of forward-backward parabolic type
An interfacial phenomenon for a class of the solutions of a nonlinear forward-backward parabolic equation in R × (0, T) is investigated. In general,...
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Global attractors for the initial value problems of Cohn-Hilliard equations on compact manifolds
In this paper we establish some theorems which are concerned with the equivalent norms of Sobolev spaces on a Riemannian manifold. Using the theorems...
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Attractors of the Dissipative Evolution Equation of the First Order in Time: Reaction—Diffusion Equations. Fluid Mechanics and Pattern Formation Equations
Our aim in this chapter is to describe some nonlinear evolution equations of the first order in time, which arise in mechanics and physics. In each...
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Exponential estimate for reaction diffusion models
We consider the superposition of a speeded up symmetric simple exclusion process with a Glauber dynamics, which leads to a reaction diffusion...
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Existence of fast traveling waves for some parabolic equations: A dynamical systems approach
We study semilinear elliptic equations δu + cu x = f(u,∇u) and δ 2 u + cu x = f(u,∇u,∇ 2 u) in infinite cylinders ( x,y ) ∃ ℝ×Ω⊂ ℝ n+1 using methods from...
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Phase Field Models With Conserved Order Parameters
In this chapter, we present a mathematical analysis of the dynamics of phase transitions with a conserved order parameter e (Model B phase...
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Phase Transitions and Hysteresis
In the previous chapters, the occurrence of hysteresis has been discussed from a mainly phenomenological and mathematical point of view. The attempt...
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An error bound for the finite element approximation of the Cahn-Hilliard equation with logarithmic free energy
An error bound is proved for a fully practical piecewise linear finite element approximation, using a backward Euler time discretization, of the...
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Onset and structure of interfaces in a Kawasaki+Glauber interacting particle system
We investigate the spatial structure of typical configurations of a reaction-diffusion spin system (Kawasaki+Glauber model), following the noise...
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Physicists’ Treatment of Catastrophes Before Catastrophe Theory
Physicists have always made use of constructions more or less equivalent to catastrophe theory in investigations of concrete problems. In this sense,...
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Curvature Dependent Phase Boundary Motion and Parabolic Double Obstacle Problems
The use of parabolic double obstacles problems for approximating curvature dependent phase boundary motion is reviewed. It is shown that such...
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Numerical analysis of the Cahn-Hilliard equation with a logarithmic free energy
A fully discrete finite element method for the Cahn-Hilliard equation with a logarithmic free energy based on the backward Euler method is analysed....
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The Approach to Equilibrium: Scaling, Universality and the Renormalisation Group
Evidence is accumulating that the long-time behaviour of certain non-equilibrium systems shows scaling behaviour. This assertion is demonstrated in...
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Low Temperature Stochastic Spin Dynamics: Metastability, Convergence to Equilibrium and Phase Segregation
I will report on recent progresses made in the rigorous study of the long time behaviour of random dynamics of physical and mathematical interest for...
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Existence for the Cahn-Hilliard phase separation model with a nondifferentiable energy
The Cahn-Hilliard model for phase separation in a binary alloy leads to the equations (I) u t =Δw, (II) w=ψ′ (u)− γΔu with an associated energy...
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Towards a Phase Field Model for Phase Transitions in Binary Alloys
To date phase field models have only been used to model non-isothermal phase transitions in a pure material. Here we describe recent steps which aim...
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Mean Field Theory of Canonical Spinodal Instabilities
We show that the character of the spinodal descomposition line of a system described by the Landau-Ginzburg theory depends on the statistical...
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Nucleation, Condensation and Evaporation in Waves and Jets
In waves and jets of real fluids at states below the critical point phase transitions often occur. These processes are called condensation and...