Young Measures in a Nonlocal Phase Transition Problem
نویسندگان
چکیده
A nonlocal variational problem modelling phase transitions is studied in the framework of Young measures. The existence of global minimisers among functions with internal layers on an infinite tube is proved by combining a weak convergence result for Young measures and the principle of concentration-compactness. The regularity of such global minimisers is discussed, and the nonlocal variational problem is also considered on asymptotic tubes.
منابع مشابه
A Time Discretization Scheme for a Nonlocal Degenerate Problem Modelling Resistance Spot Welding
In the current work we construct a nonlocal mathematical model describing the phase transition occurs during the resistance spot welding process in the industry of metallurgy. We then consider a time discretization scheme for solving the resulting nonlocal moving boundary problem. The scheme consists of solving at each time step a linear elliptic partial differential equation and then making a ...
متن کاملNumerical Computation of a Nonlocal Double Obstacle Problem
Abstract We consider a nonlocal double obstacle problem. This type of problems comes in various biological and physical situations, e.g., in phase transition models. We focus on numerical approximations and fast computation of such a model. We start with considering piece-wise basis functions for spatial approximation followed by implicit Euler’s method for time integration and then Newton’s me...
متن کاملLower Semicontinuity and Relaxation Via Young Measures for Nonlocal Variational Problems and Applications to Peridynamics
We study nonlocal variational problems in Lp, like those that appear in peridynamics. The functional object of our study is given by a double integral. We establish characterizations of weak lower semicontinuity of the functional in terms of nonlocal versions of either a convexity notion of the integrand, or a Jensen inequality for Young measures. Existence results, obtained through the direct ...
متن کاملInterference of Various Sources of Sensory Feedback on Transition of Relative Phase in Bimanual Coordination on Active and Inactive Woman With Multiple Sclerosis
Purpose: Comparing the effects of manipulating senses on relative phase transition bimanual coordination pattern of active and inactive women with Multiple Sclerosis (MS). Methods: The methodology of this study was repeated-measures design. Study participants comprised 10 active women and 10 inactive women with multiple sclerosis who voluntarily participated in this experiment. The participant...
متن کاملA Problem of Axisymmetric Vibration of Nonlocal Microstretch Thermoelastic Circular Plate with Thermomechanical Sources
In the present manuscript, we investigated a two dimensional axisymmetric problem of nonlocal microstretch thermoelastic circular plate subjected to thermomechanical sources. An eigenvalue approach is proposed to analyze the problem. Laplace and Hankel transforms are used to obtain the transformed solutions for the displacements, microrotation, microstretch, temperature distribution and stresse...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007