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81.
Matthias Röger Yoshihiro Tonegawa 《Calculus of Variations and Partial Differential Equations》2008,32(1):111-136
We prove the convergence of phase-field approximations of the Gibbs–Thomson law. This establishes a relation between the first
variation of the Van der Waals–Cahn–Hilliard energy and the first variation of the area functional. We allow for folding of
diffuse interfaces in the limit and the occurrence of higher-multiplicities of the limit energy measures. We show that the
multiplicity does not affect the Gibbs–Thomson law and that the mean curvature vanishes where diffuse interfaces have collided.
We apply our results to prove the convergence of stationary points of the Cahn–Hilliard equation to constant mean curvature
surfaces and the convergence of stationary points of an energy functional that was proposed by Ohta–Kawasaki as a model for
micro-phase separation in block-copolymers. 相似文献
82.
We prove a theorem for the existence of solutions to a variational problem, under assumptions that do not require the convexity of the integrand. 相似文献
83.
This paper studies an inverse problem of identifying the coefficient of parabolic equation when the final observation is given, which has important application in a large fields of applied science. Based on the optimal control framework, the existence and necessary condition of the minimum for the control functional are established. Since the optimal control problem is nonconvex, one may not expect a unique solution. However, in this paper the solution is proved to be locally unique. After the necessary condition is transformed into an elliptic bilateral variational inequality, an algorithm and some numerical experiments are proposed in the paper. The numerical results show that the algorithm designed in this paper is stable and that the coefficient is recovered very well. 相似文献
84.
Yisong Yang 《Letters in Mathematical Physics》1990,19(3):257-267
The main result of this note is a proof of a conjecture of Burzlaff, O'Sé and Tchrakian [1] concerning the existence of a certain kind of finite action solutions of the seven-dimensional generalized Yang-Mills-Higgs model derived from an eight-dimensional SO(8) Yang-Mills theory. 相似文献
85.
In this article,the authors obtain an integral representation for the relaxation of the functional
F(x,u,Ω):={∫^f(x,u(x),εu(x))dx Ω if u∈W^1,1(Ω,R^N), +∞ otherwise, in the space of functions of bounded deformation,with respect to L^1-convergence.Here Eu represents the absolutely continuous part of the symmetrized distributional derivative Eu.f(x,p,ξ)satisfying weak convexity assumption. 相似文献
F(x,u,Ω):={∫^f(x,u(x),εu(x))dx Ω if u∈W^1,1(Ω,R^N), +∞ otherwise, in the space of functions of bounded deformation,with respect to L^1-convergence.Here Eu represents the absolutely continuous part of the symmetrized distributional derivative Eu.f(x,p,ξ)satisfying weak convexity assumption. 相似文献
86.
Michele Carriero Antonio Leaci Franco Tomarelli 《Calculus of Variations and Partial Differential Equations》2008,32(1):81-110
We derive many necessary conditions for minimizers of a functional depending on free discontinuities, free gradient discontinuities
and second derivatives, which is related to image segmentation. 相似文献
87.
We derive estimates of the Hessian of two smooth functions defined on Grassmannian manifold. Based on it, we can derive curvature estimates for minimal submanifolds in Euclidean space via Gauss map as in [Y.L. Xin, Ling Yang, Curvature estimates for minimal submanifolds of higher codimension, arXiv: 0709.3686; 24]. In this way, the result for Bernstein type theorem done by Jost and the first author could be improved. 相似文献
88.
《Applied Mathematics and Optimization》2008,45(3):325-345
We consider the optimal control of harvesting the diffusive degenerate elliptic logistic equation. Under certain assumptions,
we prove the existence and uniqueness of an optimal control. Moreover, the optimality system and a characterization of the
optimal control are also derived. The sub-supersolution method, the singular eigenvalue problem and differentiability with
respect to the positive cone are the techniques used to obtain our results. 相似文献
89.
We consider a steady-state heat conduction problem P
α
with mixed boundary conditions for the Poisson equation depending on a positive parameter α , which represents the heat transfer coefficient on a portion Γ
1
of the boundary of a given bounded domain in R
n
. We formulate distributed optimal control problems over the internal energy g for each α . We prove that the optimal control g_ op
α
and its corresponding system u_ g_ op
α
α and adjoint p_ g_ op
α
α states for each α are strongly convergent to g
op
, u_ g
op
and p _ g
op
, respectively, in adequate functional spaces. We also prove that these limit functions are respectively the optimal control,
and the system and adjoint states corresponding to another distributed optimal control problem for the same Poisson equation
with a different boundary condition on the portion Γ
1
. We use the fixed point and elliptic variational inequality theories. 相似文献
90.
Energy-conserving algorithms are necessary to solve nonlinear elastodynamic problems in order to recover long term time integration accuracy and stability. Furthermore, some physical phenomena (such as friction) can generate dissipation; then in this work, we present and analyse two energy-consistent algorithms for hyperelastodynamic frictional contact problems which are characterised by a conserving behaviour for frictionless impacts but also by an admissible frictional dissipation phenomenon. The first approach permits one to enforce, respectively, the Kuhn–Tucker and persistency conditions during each time step by combining an adapted continuation of the Newton method and a Lagrangean formulation. In addition the second method which is based on the work in [P. Hauret, P. Le Tallec, Energy-controlling time integration methods for nonlinear elastodynamics and low-velocity impact, Comput. Methods Appl. Mech. Eng. 195 (2006) 4890–4916] represents a specific penalisation of the unilateral contact conditions. Some numerical simulations are presented to underscore the conservative or dissipative behaviour of the proposed methods. 相似文献