Search Results - "Nicholas D. Alikakos"

On the Triple Junction Problem without Symmetry Hypotheses by Alikakos, Nicholas D., Geng, Zhiyuan

“…We investigate the Allen–Cahn system Δ u - W u ( u ) = 0 , u : R 2 → R 2 , where W ∈ C 2 ( R 2 , [ 0 , + ∞ ) ) is a potential with three global minima. We…”
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Heteroclinic travelling waves of gradient diffusion systems by ALIKAKOS, NICHOLAS D., KATZOURAKIS, NIKOLAOS I.

“…We establish the existence of travelling waves to the gradient system ut = uzz — ᐁW(u) connecting two minima of W when u : ℝ x (0, ∞) → ℝN; that is, we…”
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Entire Minimizers of Allen–Cahn Systems with Sub-Quadratic Potentials by Alikakos, Nicholas D., Gazoulis, Dimitrios, Zarnescu, Arghir

“…We study entire minimizers of the Allen–Cahn systems. The specific feature of our systems are potentials having a finite number of global minima, with…”
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Entire Solutions to Equivariant Elliptic Systems with Variational Structure by Alikakos, Nicholas D., Fusco, Giorgio

“…We consider the system Δ u − W u ( u ) = 0, where , for a class of potentials that possess several global minima and are invariant under a general finite…”
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Almost entire solutions of the Burgers equation by Nicholas D. Alikakos, Dimitrios Gazoulis

“…We consider Burgers equation on the whole x-t plane. We require the solution to be classical everywhere, except possibly over a closed set S of potential…”
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SOME BASIC FACTS ON THE SYSTEM Δu - Wu(u) = 0 by ALIKAKOS, Nicholas D, YINGFEI YI

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Slow dynamics for the Cahn-Hilliard equation in higher space dimensions : The motion of bubbles by ALIKAKOS, N. D, FUSCO, G

“…It is known that the Van der Waals-Cahn-Hilliard (W-C-H) dynamics can be approximated by a Quasi-static Stefan problem with surface tension. It turns out that…”
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Some basic facts on the system \Delta u - W_{u} (u) = 0 by Alikakos, Nicholas D.

“…a priori consequences on the solutions. In particular, we point out some differences between two paradigms: the phase-transition system, with target a finite…”
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Existence of lattice solutions to semilinear elliptic systems with periodic potential by Nicholas D. Alikakos, Panayotis Smyrnelis

“…Under the assumption that the potential W is invariant under a general discrete reflection group $G'=TG$ acting on $mathbb{R}^n$, we establish existence of…”
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CONTINUUM LIMITS OF PARTICLES INTERACTING VIA DIFFUSION by Alikakos, Nicholas D., Fusco, Giorgio, Karali, Georgia

“…We consider a two‐phase system mainly in three dimensions and we examine the coarsening of the spatial distribution, driven by the reduction of interface…”
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Ostwald ripening in two dimensions—the rigorous derivation of the equations from the Mullins–Sekerka dynamics by Alikakos, Nicholas D, Fusco, Giorgio, Karali, Georgia

“…We consider a dilute mixture of a finite number of particles and we are interested in the coarsening of the spatial distribution in two space dimensions under…”
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Ostwald ripening for dilute systems under quasistationary dynamics by ALIKAKOS, Nicholas D, FUSCO, Giorgio

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Periodic traveling waves and locating oscillating patterns in multidimensional domains by Alikakos, Nicholas D., Bates, Peter W., Chen, Xinfu

“…We establish the existence and robustness of layered, time-periodic solutions to a reaction-diffusion equation in a bounded domain in \mathbb{R}^n, when the…”
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Convergence of the Cahn-Hilliard equation to the Hele-Shaw model by ALIKAKOS, N. D, BATES, P. W, XINFU CHEN

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Asymptotic behavior of the interface for entire vector minimizers in phase transitions by Alikakos, Nicholas D., Geng, Zhiyuan, Zarnescu, Arghir

“…We study globally bounded entire minimizers u:Rn→Rm of Allen-Cahn systems for potentials W≥0 with {W=0}={a1,...,aN} and W(u)∼|u−ai|α near u=ai, 0<α<2. Such…”
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The effect of the geometry of the particle distribution in ostwald ripening by ALIKAKOS, Nicholas D, FUSCO, Giorgio, KARALI, Georgia

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Motion of a droplet by surface tension along the boundary by Alikakos, Nicholas D., Chen, Xinfu, Fusco, Giorgio

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A New Proof for the Existence of an Equivariant Entire Solution Connecting the Minima of the Potential for the System Δu − W u (u) = 0 by Alikakos, Nicholas D.

“…Recently, Giorgio Fusco and the author in [ 2 ] studied the system Δu − W u (u) = 0 for a class of potentials that possess several global minima and are…”
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A New Proof for the Existence of an Equivariant Entire Solution Connecting the Minima of the Potential for the System [Delta]u - W u (u) = 0 by Alikakos, Nicholas D

“…Recently, Giorgio Fusco and the author in [2] studied the system [Delta]u - W u (u) = 0 for a class of potentials that possess several global minima and are…”
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A New Proof for the Existence of an Equivariant Entire Solution Connecting the Minima of the Potential for the System Delta u - W sub( )uu) = 0 by Alikakos, Nicholas D

“…Recently, Giorgio Fusco and the author in [2] studied the system Delta u - W sub( )uu) = 0 for a class of potentials that possess several global minima and are…”
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