On the hyperbolic relaxation of the one-dimensional Cahn–Hilliard equation☆

By Stefania Gatti, Maurizio Grasselli, Alain Miranville, Vittorino Pata. 2005

71 citations recorded by the source corpus.

Abstract We consider the one-dimensional Cahn–Hilliard equation with an inertial term ɛ u t t , for ɛ ⩾ 0 . This equation, endowed with proper boundary conditions, generates a strongly continuous semigroup S ɛ ( t ) which acts on a suitable phase-space and possesses a global attractor. Our main result is the construction of a robust family of exponential attractors { M ɛ } , whose common basins of attraction are the whole phase-space.

Subfields: Computer Networks and Communications, Control and Systems Engineering, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/17868b103a80f4fb3a2a4894edef92d896345e2c

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In Computer Networks and Communications

In Control and Systems Engineering

In Materials Chemistry

Citations in the corpus

The Cahn-Hilliard Equation with Logarithmic Potentials (2011, background): “Another important generalization of the Cahn-Hilliard equation is the hyperbolic relaxation of the equation, proposed in [103], [104], [105], [106] and [151] to model the early stages of spinodal decomposition in certain glasses (see also [26], [112], [113], [128], [129] and [130]).”
Chapter 3 Attractors for Dissipative Partial Differential Equations in Bounded and Unbounded Domains (2008, result): “(d) Based on the above results, one has been able to prove the existence of exponential attractors in many situations, see [6,7,60,61,68,70,71,74,85,100–103,105–109,116, 117,157,175–177,184], and [216].”