Asymptotic Behavior of Solutions of a Conserved Phase-Field System with Memory
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This article is published in Journal of Integral Equations and Applications.The article was published on 2003-09-01 and is currently open access. It has received 20 citations till now. The article focuses on the topics: Asymptotic analysis & Method of matched asymptotic expansions.read more
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Long Time Behavior of Solutions to the Caginalp System with Singular Potential
TL;DR: In this paper, the authors consider a nonlinear parabolic system which governs the evolution of the (relative) temperature θ and of an order parameter χ and show that any smooth and bounded trajectory uniformly converges to a stationary state and give an estimate of the decay rate.
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Asymptotic behavior of a nonisothermal viscous Cahn-Hilliard equation with inertial term
TL;DR: In this paper, the authors consider a nonisothermal fast phase separation process taking place in a three-dimensional bounded domain and prove that the corresponding dynamical system is dissipative and possesses a global attractor.
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Lyapunov functions and convergence to steady state for differential equations of fractional order
Vicente Vergara,Rico Zacher +1 more
TL;DR: In this article, the asymptotic behavior of bounded solutions to integro-differential equations in finite dimensions was studied and it was shown that any global bounded solution converges to a steady state of a related equation, if the nonlinear potential occurring in the equation satisfies the Łojasiewicz inequality.
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Uniform global attractors for non-isothermal viscous and non-viscous Cahn–Hilliard equations with dynamic boundary conditions
Ciprian G. Gal,Alain Miranville +1 more
TL;DR: In this paper, a model of non-isothermal phase separation taking place in a confined container is considered, where the order parameter ϕ is governed by a viscous or non-viscous Cahn-Hilliard type equation which is coupled with a heat equation for the temperature θ.
Journal ArticleDOI
Well-Posedness and Long Time Behavior of the Non-Isothermal Viscous Cahn-Hilliard Equation with Dynamic Boundary Conditions
TL;DR: In this article, a model of non-isothermal phase transition taking place in a conned container is considered and the order parameter is governed by a Cahn-Hilliard type equation which is coupled with a nonlinear heat equation for the temperature.