scholarly journals Convergence to a self-similar solution in general relativistic gravitational collapse

2001 ◽  
Vol 63 (8) ◽  
Author(s):  
Tomohiro Harada ◽  
Hideki Maeda
Keyword(s):  
Gravitational Collapse ◽  
Similar Solution ◽  
Self Similar Solution ◽  
General Relativistic ◽  
Self Similar

scholarly journals Larson–Penston Self-similar Gravitational Collapse

2021 ◽  
Author(s):  
Yan Guo ◽  
Mahir Hadžić ◽  
Juhi Jang
Keyword(s):  
Equation Of State ◽  
Numerical Integration ◽  
Gravitational Collapse ◽  
Similar Solution ◽  
Newtonian Gravity ◽  
Asymptotically Flat ◽  
Self Similar Solution ◽  
Self Similar ◽  
Isothermal Equation

AbstractUsing numerical integration, in 1969 Penston (Mon Not R Astr Soc 144:425–448, 1969) and Larson (Mon Not R Astr Soc 145:271–295, 1969) independently discovered a self-similar solution describing the collapse of a self-gravitating asymptotically flat fluid with the isothermal equation of state $$p=k\varrho $$ p = k ϱ , $$k>0$$ k > 0 , and subject to Newtonian gravity. We rigorously prove the existence of such a Larson–Penston solution.

On a self-similar solution for the decay of turbulent bursts

1992 ◽  
Vol 3 (4) ◽  
pp. 319-341 ◽  
Author(s):  
S. P. Hastings ◽  
L. A. Peletier
Keyword(s):  
Asymptotic Behaviour ◽  
Physical Parameter ◽  
Dimensional Analysis ◽  
Existence And Uniqueness ◽  
The Self ◽  
Similar Solution ◽  
Self Similar Solution ◽  
Eigenvalue Parameter ◽  
Self Similar ◽  
Similar Solutions

We discuss the self-similar solutions of the second kind associated with the propagation of turbulent bursts in a fluid at rest. Such solutions involve an eigenvalue parameter μ, which cannot be determined from dimensional analysis. Existence and uniqueness are established and the dependence of μ on a physical parameter λ in the problem is studied: estimates are obtained and the asymptotic behaviour as λ → ∞ is established.

Self-Similar Solution of an RC Transmission Line

1972 ◽  
Vol 40 (3) ◽  
pp. 484-486 ◽  
Author(s):  
K. E. Lonngren ◽  
W. F. Ames ◽  
H. C. S. Hsuan ◽  
I. Alexeff ◽  
William Wing
Keyword(s):  
Transmission Line ◽  
Similar Solution ◽  
Self Similar Solution ◽  
Self Similar
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