scholarly journals Hydrodynamic Limit for a Hamiltonian System with Boundary Conditions and Conservative Noise

2014 ◽  
Vol 213 (2) ◽  
pp. 561-585 ◽  
Author(s):  
Nadine Braxmeier-Even ◽  
Stefano Olla
Keyword(s):  
Hamiltonian System ◽  
Boundary Conditions ◽  
Hydrodynamic Limit ◽  
Conservative Noise

scholarly journals Hill-type formula for Hamiltonian system with Lagrangian boundary conditions

2019 ◽  
Vol 267 (4) ◽  
pp. 2416-2447
Author(s):  
Xijun Hu ◽  
Yuwei Ou ◽  
Penghui Wang
Keyword(s):  
Hamiltonian System ◽  
Boundary Conditions ◽  
Type Formula ◽  
Lagrangian Boundary

A Numerical Analytical Method for Singularity Problem in V-Type Notch

2012 ◽  
Vol 446-449 ◽  
pp. 3561-3564
Author(s):  
Chao Yang ◽  
Zhen Huan Zhou ◽  
Xin Sheng Xu
Keyword(s):  
Hamiltonian System ◽  
Stress Distribution ◽  
Boundary Conditions ◽  
Numerical Method ◽  
Analytical Method ◽  
Numerical Results ◽  
Opening Angle ◽  
Singularity Problem ◽  
Numerical Analytical Method ◽  
Special Case

In this paper, a numerical analytical method for singularity problem in V-type notch is presented based on Hamiltonian system. The method has an advantage that all boundary conditions can be considered with one model, and belongs to a general numerical method. Results show that the singularity of the problem relates to the opening angle of the V-type notch where the crack is just a special case. Further, numerical results give rules of stress distribution under various conditions.

scholarly journals Eigenvalues of stochastic Hamiltonian systems with boundary conditions and its application

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Guangdong Jing ◽  
Penghui Wang
Keyword(s):  
Hamiltonian System ◽  
Boundary Conditions ◽  
Blow Up ◽  
Time Dependent ◽  
Order Of Growth ◽  
Dependent Case ◽  
Estimation Formula ◽  
Stochastic Hamiltonian Systems ◽  
Time Invariant ◽  
Backward Sdes

<p style='text-indent:20px;'>In this paper we solve the eigenvalue problem of stochastic Hamiltonian system with boundary conditions. Firstly, we extend the results in Peng [<xref ref-type="bibr" rid="b12">12</xref>] from time-invariant case to time-dependent case, proving the existence of a series of eigenvalues <inline-formula><tex-math id="M1">\begin{document}$ \{\lambda_m\} $\end{document}</tex-math></inline-formula> and construct corresponding eigenfunctions. Moreover, the order of growth for these <inline-formula><tex-math id="M2">\begin{document}$ \{\lambda_m\} $\end{document}</tex-math></inline-formula> are obtained: <inline-formula><tex-math id="M3">\begin{document}$ \lambda_m\sim m^2 $\end{document}</tex-math></inline-formula>, as <inline-formula><tex-math id="M4">\begin{document}$ m\rightarrow +\infty $\end{document}</tex-math></inline-formula>. As applications, we give an explicit estimation formula about the statistic period of solutions of Forward-Backward SDEs. Besides, by a meticulous example we show the subtle situation in time-dependent case that some eigenvalues appear when the solution of the associated Riccati equation does not blow-up, which does not happen in time-invariant case.</p>

Sign in / Sign up

Export Citation Format

Share Document