Young Measure Solutions for Nonconvex Elastodynamics
نویسندگان
چکیده
منابع مشابه
Adaptive Approximation of Young Measure Solutions in Scalar Nonconvex Variational Problems
This paper addresses the numerical approximation of Young measures appearing as generalized solutions to scalar nonconvex variational problems. We prove a priori and a posteriori error estimates for a macroscopic quantity, the stress. For a scalar three-well problem we show convergence of other quantities such as Young measure support and microstructure region. Numerical experiments indicate th...
متن کاملYoung-measure Approximations for Elastodynamics with Non-monotone Stress-strain Relations
Microstructures in phase-transitions of alloys are modeled by the energy minimization of a nonconvex energy density φ. Their time-evolution leads to a nonlinear wave equation utt = div S(Du) with the non-monotone stress-strain relation S = Dφ plus proper boundary and initial conditions. This hyperbolic-elliptic initial-boundary value problem of changing types allows, in general, solely Youngmea...
متن کاملFlow properties for Young{measure solutions of semilinear hyperbolic problems
For hyperbolic systems in one spatial dimension @ t u+C@ x u = f(u), u(t; x) 2 R d , we study sequences of oscillating solutions by their Young{measure limit and develop tools to study the evolution of directly from the Young measure of the initial data. For d 2 we construct a ow mapping S t such that (t) = S t () is the unique Young measure solution for initial value. For d 3 we establish exis...
متن کاملWeak Solutions for One-dimensional Non-convex Elastodynamics
We explore local existence and properties of classical weak solutions to the initial-boundary value problem of a one-dimensional quasilinear equation of elastodynamics with non-convex stored-energy function, a model of phase transitions in elastic bars proposed by Ericksen [19]. The instantaneous formation of microstructures of local weak solutions is observed for all smooth initial data with i...
متن کاملSolutions and optimality criteria for nonconvex quadratic-exponential minimization problem
This paper presents a set of complete solutions and optimality conditions for a nonconvex quadratic-exponential optimization problem. By using the canonical duality theory developed by the first author, the nonconvex primal problem in n-dimensional space can be converted into an one-dimensional canonical dual problem with zero duality gap, which can be solved easily to obtain all dual solutions...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Mathematical Analysis
سال: 2003
ISSN: 0036-1410,1095-7154
DOI: 10.1137/s0036141001392141