scholarly journals Finite Time Singularities for Hyperbolic Systems

2015 ◽  
Vol 47 (1) ◽  
pp. 758-785 ◽  
Author(s):  
Geng Chen ◽  
Tao Huang ◽  
Chun Liu
Keyword(s):  
Finite Time ◽  
Hyperbolic Systems ◽  
Time Singularities

scholarly journals Finite-time stabilization in optimal time of homogeneous quasilinear hyperbolic systems in one dimensional space

2020 ◽  
Vol 26 ◽  
pp. 119 ◽  
Author(s):  
Jean-Michel Coron ◽  
Hoai-Minh Nguyen
Keyword(s):  
Finite Time ◽  
Nonlinear Boundary ◽  
Dimensional Space ◽  
Hyperbolic Systems ◽  
Optimal Time ◽  
Local Boundary ◽  
Quasilinear Hyperbolic Systems ◽  
Non Local ◽  
Linearized System ◽  
Finite Time Stabilization

We consider the finite-time stabilization of homogeneous quasilinear hyperbolic systems with one side controls and with nonlinear boundary condition at the other side. We present time-independent feedbacks leading to the finite-time stabilization in any time larger than the optimal time for the null controllability of the linearized system if the initial condition is sufficiently small. One of the key technical points is to establish the local well-posedness of quasilinear hyperbolic systems with nonlinear, non-local boundary conditions.

scholarly journals Finite time singularities for the free boundary incompressible Euler equations

2013 ◽  
Vol 178 (3) ◽  
pp. 1061-1134 ◽  
Author(s):  
Angel Castro ◽  
Diego Córdoba ◽  
Charles Fefferman ◽  
Francisco Gancedo ◽  
Javier Gómez-Serrano
Keyword(s):  
Free Boundary ◽  
Euler Equations ◽  
Finite Time ◽  
Incompressible Euler Equations ◽  
Time Singularities ◽  
Incompressible Euler

scholarly journals RICCI LOWER BOUND FOR KÄHLER–RICCI FLOW

2014 ◽  
Vol 16 (02) ◽  
pp. 1350053 ◽  
Author(s):  
ZHOU ZHANG
Keyword(s):  
Lower Bound ◽  
Ricci Curvature ◽  
Ricci Flow ◽  
Finite Time ◽  
Ricci Flows ◽  
Time Singularities

We provide general discussion on the lower bound of Ricci curvature along Kähler–Ricci flows over closed manifolds. The main result is the non-existence of Ricci lower bound for flows with finite time singularities and non-collapsed global volume. As an application, we give examples showing that positivity of Ricci curvature would not be preserved by Ricci flow in general.

scholarly journals Finite-time singularities in f(R, T) gravity and the effect of conformal anomaly

2013 ◽  
Vol 91 (7) ◽  
pp. 548-553 ◽  
Author(s):  
M.J.S. Houndjo ◽  
C.E.M. Batista ◽  
J.P. Campos ◽  
O.F. Piattella
Keyword(s):  
Finite Time ◽  
Cosmic Acceleration ◽  
Gravity Models ◽  
Conformal Anomaly ◽  
Energy Tensor ◽  
Big Rip ◽  
Stress Energy ◽  
Time Singularities ◽  
Two Parameters ◽  
Suitable Expression

We investigate f(R, T) gravity models (where R is the curvature scalar and T is the trace of the stress–energy tensor of ordinary matter) that are able to reproduce the four known types of future finite-time singularities. We choose a suitable expression for the Hubble parameter to realise the cosmic acceleration and we introduce two parameters, α and Hs, which characterise each type of singularity. We address the conformal anomaly and we observe that it cannot remove the sudden singularity or the Big Brake, but, for some values of α, the Big Rip and the Big Freeze may be avoided. We also find that, even without taking into account the conformal anomaly, the Big Rip and the Big Freeze may be removed thanks to the presence of the T contribution of the f(R, T) theory.

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