scholarly journals A note on local higher regularity in the dynamic linear relaxed micromorphic model

2021 ◽  
Author(s):  
Sebastian Owczarek ◽  
Ionel‐Dumitrel Ghiba ◽  
Patrizio Neff
Keyword(s):  
Higher Regularity

scholarly journals Strong Uniform Attractors for Nonautonomous Suspension Bridge-Type Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-19
Author(s):  
Xuan Wang ◽  
Qiaozhen Ma
Keyword(s):  
Hilbert Space ◽  
Dynamical Behavior ◽  
Type Equation ◽  
Strong Solutions ◽  
Suspension Bridge ◽  
Bridge Type ◽  
Uniform Attractors ◽  
External Forces ◽  
Higher Regularity

We discuss long-term dynamical behavior of the solutions for the nonautonomous suspension bridge-type equation in the strong Hilbert spaceD(A)×H2(Ω)∩H01(Ω), where the nonlinearityg(u,t)is translation compact and the time-dependent external forcesh(x,t)only satisfy condition (C*) instead of translation compact. The existence of strong solutions and strong uniform attractors is investigated using a new process scheme. Since the solutions of the nonautonomous suspension bridge-type equation have no higher regularity and the process associated with the solutions is not continuous in the strong Hilbert space, the results are new and appear to be optimal.

scholarly journals Modeling and Algorithms of the Crew Rostering Problem with Given Cycle on High-Speed Railway Lines

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Zhiqiang Tian ◽  
Huimin Niu
Keyword(s):  
High Speed ◽  
Ant Colony Algorithm ◽  
Set Covering ◽  
Covering Problem ◽  
High Speed Railway ◽  
Crew Rostering ◽  
Crew Rostering Problem ◽  
Plan Making ◽  
Higher Regularity ◽  
Improved Ant Colony Algorithm

This paper studies the modeling and algorithms of crew roster problem with given cycle on high-speed railway lines. Two feasible compilation strategies for work out the crew rostering plan are discussed, and then an integrated compilation method is proposed in this paper to obtain a plan with relatively higher regularity in execution and lower crew members arranged. The process of plan making is divided into two subproblems which are decomposition of crew legs and adjustment of nonmaximum crew roster scheme. The decomposition subproblem is transformed to finding a Hamilton chain with the best objective function in network which was solved by an improved ant colony algorithm, whereas the adjustment of nonmaximum crew rostering scheme is finally presented as a set covering problem and solved by a two-stage algorithm. The effectiveness of the proposed models and algorithms are testified by a numerical example.

scholarly journals Regularity and approximation of strong solutions to rate-independent systems

2017 ◽  
Vol 27 (13) ◽  
pp. 2511-2556 ◽  
Author(s):  
Filip Rindler ◽  
Sebastian Schwarzacher ◽  
Endre Süli
Keyword(s):  
Strong Solutions ◽  
Local Convexity ◽  
Finite Element Discretization ◽  
Elliptic Regularity ◽  
Element Discretization ◽  
Fully Discrete ◽  
Regularity Estimates ◽  
Mathematical Techniques ◽  
Regularity Results ◽  
Higher Regularity

Rate-independent systems arise in a number of applications. Usually, weak solutions to such problems with potentially very low regularity are considered, requiring mathematical techniques capable of handling nonsmooth functions. In this work, we prove the existence of Hölder-regular strong solutions for a class of rate-independent systems. We also establish additional higher regularity results that guarantee the uniqueness of strong solutions. The proof proceeds via a time-discrete Rothe approximation and careful elliptic regularity estimates depending in a quantitative way on the (local) convexity of the potential featuring in the model. In the second part of the paper, we show that our strong solutions may be approximated by a fully discrete numerical scheme based on a spatial finite element discretization, whose rate of convergence is consistent with the regularity of strong solutions whose existence and uniqueness are established.

scholarly journals Optimal bilinear control of eddy current equations with grad–div regularization

2015 ◽  
Vol 23 (1) ◽  
Author(s):  
Irwin Yousept
Keyword(s):  
Optimal Control ◽  
Control Problem ◽  
Electric Conductivity ◽  
Eddy Current ◽  
Regularity Property ◽  
Control Approach ◽  
Bilinear Control ◽  
Time Harmonic ◽  
Eddy Current Equations ◽  
Higher Regularity

AbstractAn optimal bilinear control problem governed by time-harmonic eddy current equations is considered to estimate the electric conductivity of a 3D bounded isotropic domain. The model problem is mainly complicated by the possible presence of non-conducting materials in the domain. We introduce an optimal control approach based on grad-div regularization and divergence penalization. The estimation for the electric conductivity obtained by solving the optimal control problem is allowed to be discontinuous. Here, no higher regularity property can be derived from the corresponding optimality conditions. We analyze the approach and present various numerical results exhibiting its numerical performance

Sign in / Sign up

Export Citation Format

Share Document