Infinite-time singularities models and possible avoidance

2021 ◽  
pp. 168569
Author(s):  
R.D. Boko ◽  
I.G. Salako
Keyword(s):  
Infinite Time ◽  
Time Singularities

Interacting cosmological viscous fluid with Little Rip and Pseudo Rip solutions in f(R) gravity

2018 ◽  
Vol 15 (02) ◽  
pp. 1850028 ◽  
Author(s):  
R. D. Boko ◽  
M. J. S. Houndjo ◽  
J. Tossa
Keyword(s):  
Dark Matter ◽  
Dark Energy ◽  
Equation Of State ◽  
Viscous Fluid ◽  
Modified Gravity ◽  
Infinite Time ◽  
Two Fluids ◽  
Viscosity Models ◽  
Time Singularities ◽  
Analytic Expressions

In this paper, we investigate the evolution of the equation of state of the interacting viscous dark energy in [Formula: see text] gravity. We first consider the case when the dark energy does not interact with the dark matter and after, the case where there is a coupling between these dark components. The viscosity and the interaction between the two fluids are parameterized by constants [Formula: see text] and [Formula: see text] respectively for which a detailed investigation on the cosmological implications has been done. In the later part of the paper, we explore some bulk viscosity models with Little and Pseudo Rip infinite time singularities within [Formula: see text] modified gravity. We obtain analytic expressions for characteristic properties of these cosmological models.

scholarly journals Cosmological viscous fluid models describing infinite time singularities in f(T) gravity

2020 ◽  
Vol 80 (9) ◽  
Author(s):  
R. D. Boko ◽  
M. J. S. Houndjo
Keyword(s):  
Dark Energy ◽  
Equations Of Motion ◽  
State Parameter ◽  
Infinite Time ◽  
Constant Deceleration Parameter ◽  
Two Fluids ◽  
Viscosity Models ◽  
Time Singularities ◽  
Analytic Expressions ◽  
Gravitational Equations

AbstractIn this paper we explore the state parameter behaviour of the interacting viscous dark energy in f(T) gravity. Using constant deceleration parameter we investigate the cosmological implications of the viscosity and interaction between the dark components (energy and matter) in terms of Redshift. So doing, the viscosity and the interaction between the two fluids are parameterized by constants $$\delta $$ δ and $$\xi $$ ξ respectively. In the later part of the paper, we explore some bulk viscosity models describing Little Rip and Pseudo Rip future singularities within f(T) modified gravity. We obtain gravitational equations of motion for viscous dark energy coupled with dark matter. Solving these equations, we found analytic expressions for characteristic properties of these cosmological models.

scholarly journals General weak limit for Kähler–Ricci flow

2016 ◽  
Vol 18 (05) ◽  
pp. 1550079
Author(s):  
Zhou Zhang
Keyword(s):  
Evolution Equation ◽  
Ricci Flow ◽  
Weak Limit ◽  
Infinite Time ◽  
Time Singularity ◽  
Ricci Flows ◽  
Sequential Convergence ◽  
Minimal Singularity ◽  
Flow Limit ◽  
Time Singularities

Consider the Kähler–Ricci flow with finite time singularities over any closed Kähler manifold. We prove the existence of the flow limit in the sense of current toward the time of singularity. This answers affirmatively a problem raised by Tian in [New results and problems on Kähler–Ricci flow, Astérisque 322 (2008) 71–92] on the uniqueness of the weak limit from sequential convergence construction. The notion of minimal singularity introduced by Demailly in the study of positive current comes up naturally. We also provide some discussion on the infinite time singularity case for comparison. The consideration can be applied to more flexible evolution equation of Kähler–Ricci flow type for any cohomology class. The study is related to general conjectures on the singularities of Kähler–Ricci flows.

scholarly journals Infinite-time singularities of the Kähler–Ricci flow

2015 ◽  
Vol 19 (5) ◽  
pp. 2925-2948 ◽  
Author(s):  
Valentino Tosatti ◽  
Yuguang Zhang
Keyword(s):  
Ricci Flow ◽  
Infinite Time ◽  
Time Singularities

Infinite time blow-up for half-harmonic map flow from R into S1

2021 ◽  
Vol 143 (4) ◽  
pp. 1261-1335
Author(s):  
Yannick Sire ◽  
Juncheng Wei ◽  
Youquan Zheng
Keyword(s):  
Blow Up ◽  
Harmonic Map ◽  
Infinite Time ◽  
Harmonic Map Flow

scholarly journals Nonlinear evolution problems with singular coefficients in the lower order terms

2021 ◽  
Vol 28 (4) ◽  
Author(s):  
Fernando Farroni ◽  
Luigi Greco ◽  
Gioconda Moscariello ◽  
Gabriella Zecca
Keyword(s):  
Lower Order ◽  
Time Horizon ◽  
Existence Result ◽  
Nonlinear Evolution ◽  
Order Term ◽  
Time Behavior ◽  
Infinite Time ◽  
Singular Coefficient ◽  
Singular Coefficients ◽  
Lower Order Terms

AbstractWe consider a Cauchy–Dirichlet problem for a quasilinear second order parabolic equation with lower order term driven by a singular coefficient. We establish an existence result to such a problem and we describe the time behavior of the solution in the case of the infinite–time horizon.

scholarly journals Global existence, energy decay and blow-up of solutions for wave equations with time delay and logarithmic source

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Sun-Hye Park
Keyword(s):  
Time Delay ◽  
Global Existence ◽  
Wave Equations ◽  
Blow Up ◽  
Logarithmic Sobolev Inequality ◽  
Decay Rates ◽  
Infinite Time ◽  
Global Existence Of Solutions ◽  
Frictional Damping ◽  
T Tau

AbstractIn this paper, we study the wave equation with frictional damping, time delay in the velocity, and logarithmic source of the form $$ u_{tt}(x,t) - \Delta u (x,t) + \alpha u_{t} (x,t) + \beta u_{t} (x, t- \tau ) = u(x,t) \ln \bigl\vert u(x,t) \bigr\vert ^{\gamma } . $$ u t t ( x , t ) − Δ u ( x , t ) + α u t ( x , t ) + β u t ( x , t − τ ) = u ( x , t ) ln | u ( x , t ) | γ . There is much literature on wave equations with a polynomial nonlinear source, but not much on the equations with logarithmic source. We show the local and global existence of solutions using Faedo–Galerkin’s method and the logarithmic Sobolev inequality. And then we investigate the decay rates and infinite time blow-up for the solutions through the potential well and perturbed energy methods.

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