Optimal control of the sixth-order convective Cahn-Hilliard equation
نویسندگان
چکیده
منابع مشابه
The convective Cahn-Hilliard equation
We consider the convective Cahn–Hilliard equation with periodic boundary conditions as an infinite dimensional dynamical system and establish the existence of a compact attractor and a finite dimensional inertial manifold that contains it. Moreover, Gevrey regularity of solutions on the attractor is established and used to prove that four nodes are determining for each solution on the attractor...
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In this article, we study the initial-boundary-value problem for a sixth-order Cahn-Hilliard type equation ut = D μ, μ = γDu− a(u)Du− a′(u) 2 |Du| + f(u) + kut, which describes the separation properties of oil-water mixtures, when a substance enforcing the mixing of the phases is added. The optimal control of the sixth order Cahn-Hilliard type equation under boundary condition is given and the ...
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A convective Cahn-Hilliard type equation of sixth order that describes the faceting of a growing surface is considered with periodic boundary conditions. By using a Galerkin approach the existence of weak solutions to this sixth order partial differential equation is established in L2(0, T ; Ḣ3 per). Furthermore stronger regularity results have been derived and these are used to prove uniquenes...
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In this paper we study a distributed optimal control problem for a nonlocal convective Cahn–Hilliard equation with degenerate mobility and singular potential in three dimensions of space. While the cost functional is of standard tracking type, the control problem under investigation cannot easily be treated via standard techniques for two reasons: the state system is a highly nonlinear system o...
متن کاملCoarsening dynamics of the convective Cahn-Hilliard equation
We characterize the coarsening dynamics associated with a convective Cahn-Hilliard equation (cCH) in one space dimension. First, we derive a sharp-interface theory through a matched asymptotic analysis. Two types of phase boundaries (kink and anti-kink) arise, due to the presence of convection, and their motions are governed to leading order by a nearest-neighbors interaction coarsening dynamic...
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ژورنال
عنوان ژورنال: Boundary Value Problems
سال: 2014
ISSN: 1687-2770
DOI: 10.1186/s13661-014-0206-3