scholarly journals A lower bound for the blow-up time to a viscoelastic hyperbolic equation with nonlinear sources

2016 ◽  
Vol 60 ◽  
pp. 115-119 ◽  
Author(s):  
Bin Guo ◽  
Fang Liu
Keyword(s):  
Lower Bound ◽  
Hyperbolic Equation ◽  
Blow Up

scholarly journals A lower bound for blow-up time in a fully parabolic Keller–Segel system

2013 ◽  
Vol 26 (4) ◽  
pp. 510-514 ◽  
Author(s):  
Jingru Li ◽  
Sining Zheng
Keyword(s):  
Lower Bound ◽  
Blow Up

Lower bound for the perimeter density at singular points of a minimizing cluster in ℝN

2020 ◽  
Vol 26 ◽  
pp. 1
Author(s):  
Jonas Hirsch ◽  
Michele Marini
Keyword(s):  
Lower Bound ◽  
Blow Up ◽  
Singular Points ◽  
Sharp Lower Bound

In this paper, we study the blow-ups of the singular points in the boundary of a minimizing cluster lying in the interface of more than two chambers. We establish a sharp lower bound for the perimeter density at those points and we prove that this bound is rigid, namely having the lowest possible density completely characterizes the blow-up.

scholarly journals BÜCHI COMPLEMENTATION MADE TIGHTER

2006 ◽  
Vol 17 (04) ◽  
pp. 851-867 ◽  
Author(s):  
EHUD FRIEDGUT ◽  
ORNA KUPFERMAN ◽  
MOSHE Y. VARDI
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Blow Up ◽  
Careful Analysis ◽  
Point Of View ◽  
Upper And Lower Bounds ◽  
Theoretical Point ◽  
Infinite Words ◽  
Büchi Automata ◽  
Buchi Automata

The complementation problem for nondeterministic word automata has numerous applications in formal verification. In particular, the language-containment problem, to which many verification problems is reduced, involves complementation. For automata on finite words, which correspond to safety properties, complementation involves determinization. The 2n blow-up that is caused by the subset construction is justified by a tight lower bound. For Büchi automata on infinite words, which are required for the modeling of liveness properties, optimal complementation constructions are quite complicated, as the subset construction is not sufficient. From a theoretical point of view, the problem is considered solved since 1988, when Safra came up with a determinization construction for Büchi automata, leading to a 2O(n log n) complementation construction, and Michel came up with a matching lower bound. A careful analysis, however, of the exact blow-up in Safra's and Michel's bounds reveals an exponential gap in the constants hiding in the O( ) notations: while the upper bound on the number of states in Safra's complementary automaton is n2n, Michel's lower bound involves only an n! blow up, which is roughly (n/e)n. The exponential gap exists also in more recent complementation constructions. In particular, the upper bound on the number of states in the complementation construction of Kupferman and Vardi, which avoids determinization, is (6n)n. This is in contrast with the case of automata on finite words, where the upper and lower bounds coincides. In this work we describe an improved complementation construction for nondeterministic Büchi automata and analyze its complexity. We show that the new construction results in an automaton with at most (0.96n)n states. While this leaves the problem about the exact blow up open, the gap is now exponentially smaller. From a practical point of view, our solution enjoys the simplicity of the construction of Kupferman and Vardi, and results in much smaller automata.

scholarly journals A blow-up result for a higher-order nonlinear Kirchhoff-type hyperbolic equation

2007 ◽  
Vol 20 (8) ◽  
pp. 866-871 ◽  
Author(s):  
Salim A. Messaoudi ◽  
Belkacem Said Houari
Keyword(s):  
Hyperbolic Equation ◽  
Blow Up ◽  
Higher Order ◽  
Kirchhoff Type
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