Upper and lower bounds of blow-up time to a parabolic type Kirchhoff equation with arbitrary initial energy

2018 ◽  
Vol 76 (10) ◽  
pp. 2477-2483 ◽  
Author(s):  
Yuzhu Han ◽  
Wenjie Gao ◽  
Zhe Sun ◽  
Haixia Li
Keyword(s):  
Lower Bounds ◽  
Blow Up ◽  
Parabolic Type ◽  
Initial Energy ◽  
Kirchhoff Equation ◽  
Upper And Lower Bounds

scholarly journals Blow-up phenomena for the sixth-order Boussinesq equation with fourth-order dispersion term and nonlinear source

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Jinxing Liu ◽  
Xiongrui Wang ◽  
Jun Zhou ◽  
Huan Zhang
Keyword(s):  
Lower Bounds ◽  
Fourth Order ◽  
Boussinesq Equation ◽  
Blow Up ◽  
Sixth Order ◽  
Upper And Lower Bounds ◽  
Differential Inequalities ◽  
Nonlinear Source ◽  
Order Dispersion ◽  
Dispersion Term

<p style='text-indent:20px;'>This paper deals with the sixth-order Boussinesq equation with fourth-order dispersion term and nonlinear source. By using some ordinary differential inequalities, the conditions on finite time blow-up of solutions are given with suitable assumptions on initial values. Moreover, the upper and lower bounds of the blow-up time are also investigated.</p>

scholarly journals SOME COMPACTNESS RESULTS RELATED TO SCALAR CURVATURE DEFORMATION

2007 ◽  
Vol 09 (01) ◽  
pp. 81-120 ◽  
Author(s):  
YU YAN
Keyword(s):  
Scalar Curvature ◽  
Lower Bounds ◽  
Blow Up ◽  
Upper And Lower Bounds ◽  
Conformally Flat ◽  
Conformally Flat Manifolds ◽  
Locally Conformally Flat ◽  
Curvature Deformation ◽  
Flat Manifolds ◽  
Curvature Problem

Motivated by the prescribing scalar curvature problem, we study the equation [Formula: see text] on locally conformally flat manifolds (M,g) with R(g) ≡ 0. We prove that when K satisfies certain conditions and the dimension of M is 3 or 4, any positive solution u of this equation with bounded energy has uniform upper and lower bounds. Similar techniques can also be applied to prove that on four-dimensional locally conformally flat scalar positive manifolds the solutions of [Formula: see text] can only have simple blow-up points.

scholarly journals Critical initial conditions for spatially-distributed thermal explosions

1992 ◽  
Vol 33 (3) ◽  
pp. 350-362 ◽  
Author(s):  
A. A. Lacey ◽  
G. C. Wake
Keyword(s):  
Initial Data ◽  
Global Existence ◽  
Lower Bounds ◽  
Blow Up ◽  
Initial Conditions ◽  
Minimal Solution ◽  
Upper And Lower Bounds ◽  
Spatially Distributed ◽  
Thermal Explosions ◽  
New Criteria

AbstractThe problem of finding critical initial data which separate conditions leading to blow-up from those which give solutions tending to the (stable) minimal solution is considered. New criteria for blow-up and global existence are found; these are equivalent to obtaining upper and lower bounds respectively for the set of critical initial data.

scholarly journals Qualitative analysis of solutions for a parabolic type Kirchhoff equation with logarithmic nonlinearity

2021 ◽  
Vol 4 (2) ◽  
pp. 1-10
Author(s):  
Erhan Pişkin ◽  
◽  
Tuğrul Cömert ◽  
Keyword(s):  
Weak Solution ◽  
Boundary Value Problem ◽  
Blow Up ◽  
Parabolic Type ◽  
Initial Boundary ◽  
Global Weak Solution ◽  
Initial Boundary Value Problem ◽  
Kirchhoff Equation ◽  
Potential Wells ◽  
Initial Boundary Value

In this work, we investigate the initial boundary-value problem for a parabolic type Kirchhoff equation with logarithmic nonlinearity. We get the existence of global weak solution, by the potential wells method and energy method. Also, we get results of the decay and finite time blow up of the weak solutions.

scholarly journals On the Generalized Distance Energy of Graphs

Mathematics ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 17 ◽  
Author(s):  
Abdollah Alhevaz ◽  
Maryam Baghipur ◽  
Hilal A. Ganie ◽  
Yilun Shang
Keyword(s):  
Lower Bounds ◽  
Complete Graph ◽  
Connected Graph ◽  
Distance Matrix ◽  
Wiener Index ◽  
Diagonal Matrix ◽  
Upper And Lower Bounds ◽  
Star Graph ◽  
Extremal Graphs ◽  
Generalized Distance

The generalized distance matrix D α ( G ) of a connected graph G is defined as D α ( G ) = α T r ( G ) + ( 1 − α ) D ( G ) , where 0 ≤ α ≤ 1 , D ( G ) is the distance matrix and T r ( G ) is the diagonal matrix of the node transmissions. In this paper, we extend the concept of energy to the generalized distance matrix and define the generalized distance energy E D α ( G ) . Some new upper and lower bounds for the generalized distance energy E D α ( G ) of G are established based on parameters including the Wiener index W ( G ) and the transmission degrees. Extremal graphs attaining these bounds are identified. It is found that the complete graph has the minimum generalized distance energy among all connected graphs, while the minimum is attained by the star graph among trees of order n.

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