English
Related papers

Related papers: Optimal temperature distribution for a nonisotherm…

200 papers

In this paper, we study a distributed optimal control problem for a diffuse interface model for tumor growth. The model consists of a Cahn-Hilliard type equation for the phase field variable coupled to a reaction diffusion equation for the…

Optimization and Control · Mathematics 2021-10-12 Matthias Ebenbeck , Patrik Knopf

We investigate the Cahn-Hilliard equation with nonlinear diffusion and non-degenerate mobility modeling phase separation phenomena in complex systems (e.g., crystals and polymers). Previous results in the literature on this model relied on…

Analysis of PDEs · Mathematics 2025-10-10 Monica Conti , Stefania Gatti , Andrea Giorgini , Giulio Schimperna

To describe the simultaneous order-disorder transformation and phase separation Eguchi, Oki and Matsumura [\doi{10.1557/proc-21-589}] introduced the system of two equations: one equation, governing the evolution of a conserved order…

Statistical Mechanics · Physics 2025-11-19 P. O. Mchedlov-Petrosyan , L. N. Davydov

Nonequlibrium phase transition of an open Takayama-Lin Liu-Maki chain coupled with two reservoirs is investigated by combining a mean-field approximation and a formula characterizing nonequlibrium steady states, which is obtained from the…

Statistical Mechanics · Physics 2013-09-24 Shigeru Ajisaka , Hisashi Nishimura , Shuichi Tasaki , Ichiro Terasaki

In this paper we propose and analyze an energy stable numerical scheme for the Cahn-Hilliard equation, with second order accuracy in time and the fourth order finite difference approximation in space. In particular, the truncation error for…

Numerical Analysis · Mathematics 2017-12-19 Kelong Cheng , Wenqiang Feng , Cheng Wang , Steven M. Wise

In this paper, we address an optimal distributed control problem for a non-local model of phase-field type, describing the evolution of tumour cells in presence of a nutrient. The model couples a non-local and viscous Cahn-Hilliard equation…

Analysis of PDEs · Mathematics 2023-10-25 Matteo Fornoni

In this paper, we investigate a distributed optimal control problem for a convective viscous Cahn-Hilliard system with dynamic boundary conditions. Such systems govern phase separation processes between two phases taking place in an…

Analysis of PDEs · Mathematics 2017-09-13 Pierluigi Colli , Gianni Gilardi , Jürgen Sprekels

We consider a non-local tumour growth model of phase-field type, describing the evolution of tumour cells through proliferation in presence of a nutrient. The model consists of a coupled system, incorporating a non-local Cahn-Hilliard…

Analysis of PDEs · Mathematics 2024-07-29 Matteo Fornoni

In this paper we present a mathematical model to describe the phenomenon of phase separation, which is modelled as space regions where an order parameter changes smoothly. The model proposed, including thermal and mixing effects, is deduced…

Mathematical Physics · Physics 2011-02-08 Alessia Berti , Ivana Bochicchio

In this work, we investigate a distributed optimal control problem for an extended phase field system of Cahn--Hilliard type which physical context is that of tumor growth dynamics. In a previous contribution, the author has already studied…

Analysis of PDEs · Mathematics 2019-08-30 Andrea Signori

The Cahn--Hilliard equation is a fundamental model that describes phase separation processes of binary mixtures. In recent years, several types of dynamic boundary conditions have been proposed in order to account for possible short-range…

Analysis of PDEs · Mathematics 2023-07-28 Chun Liu , Hao Wu

In this study, we evaluate the performance of feedback control-based time step adaptivity schemes for the nonlocal Cahn-Hilliard equation derived from the Ohta-Kawasaki free energy functional. The temporal adaptivity scheme is recast under…

Computational Engineering, Finance, and Science · Computer Science 2020-10-01 Gabriel F. Barros , Adriano M. A. Côrtes , Alvaro L. G. A. Coutinho

In this paper, we consider the numerical approximations for the commonly used binary fluid-surfactant phase field model that consists two nonlinearly coupled Cahn-Hilliard equations. The main challenge in solving the system numerically is…

Numerical Analysis · Mathematics 2017-03-20 Xiaofeng Yang

Nonadiabatic unitary evolution with tailored time-dependent Hamiltonians can prepare systems of cold atomic gases with various desired properties. For a system of two one-dimensional quasicondensates coupled with a time-varying tunneling…

Quantum Gases · Physics 2013-04-09 Armin Rahmani , Takuya Kitagawa , Eugene Demler , Claudio Chamon

A distributed optimal control problem for a phase field system which physical context is that of tumor growth is discussed. The system we are going to take into account consists of a Cahn-Hilliard equation for the phase variable (relative…

Analysis of PDEs · Mathematics 2021-01-20 Andrea Signori

In this paper, we carry out stability and error analyses for two first-order, semi-discrete time stepping schemes, which are based on the newly developed Invariant Energy Quadratization approach, for solving the well-known Cahn-Hilliard and…

Numerical Analysis · Mathematics 2017-12-08 Xiaofeng Yang , Guodong Zhang

We present a finite-volume based numerical scheme for a nonlocal Cahn-Hilliard equation which combines ideas from recent numerical schemes for gradient flow equations and nonlocal Cahn-Hilliard equations. The equation of interest is a…

Numerical Analysis · Mathematics 2024-04-08 Rainey Lyons , Grigor Nika , Adrian Muntean

We address an optimal control problem governed by a system coupling a Brinkman-type momentum equation for the velocity field with a sixth-order Cahn-Hilliard equation for the phase variable, incorporating curvature effects in the free…

Optimization and Control · Mathematics 2026-01-12 Pierluigi Colli , Gianni Gilardi , Andrea Signori , Jürgen Sprekels

In this paper we consider an energy storage optimization problem in finite time in a model with partial information that allows for a changing economic environment. The state process consists of the storage level controlled by the storage…

Mathematical Finance · Quantitative Finance 2016-06-21 Anton A. Shardin , Michaela Szölgyenyi

We are concerned with the simulation and control of a two phase flow model governed by a coupled Cahn-Hilliard Navier-Stokes system involving a nonsmooth energy potential. We establish the existence of optimal solutions and present two…

Optimization and Control · Mathematics 2019-07-10 Carmen Gräßle , Michael Hintermüller , Michael Hinze , Tobias Keil