GLOBAL EXISTENCE TO THE EINSTEIN-SCALAR FIELD SYSTEM ON THE ROBERTSON–WALKER SPACE-TIMES WITH HYPERBOLIC AND SPHERICAL SYMMETRIES

2010 ◽  
Vol 07 (01) ◽  
pp. 69-83
Author(s):  
NORBERT NOUTCHEGUEME ◽  
ALEXIS NANGUE
Keyword(s):  
Asymptotic Behavior ◽  
Scalar Field ◽  
Global Existence ◽  
Initial Velocity ◽  
Existence Of Solutions ◽  
Expansion Factor ◽  
Positive Cosmological Constant ◽  
Field System ◽  
Global Existence Of Solutions ◽  
Cosmological Expansion

Global existence of solutions is proved and asymptotic behavior is investigated, in the case of a positive cosmological constant and positive initial velocity of the cosmological expansion factor.

scholarly journals Blow-up and global existence for a kinetic equation of swarm formation

2017 ◽  
Vol 27 (06) ◽  
pp. 1153-1175 ◽  
Author(s):  
Mirosław Lachowicz ◽  
Henryk Leszczyński ◽  
Martin Parisot
Keyword(s):  
Asymptotic Behavior ◽  
Kinetic Equation ◽  
Global Existence ◽  
Integral Operator ◽  
Blow Up ◽  
Existence Of Solutions ◽  
Interaction Rate ◽  
Global Existence Of Solutions ◽  
Nonlinear Integral Operator ◽  
The Right

In this paper we study a kinetic equation that describes swarm formations. The right-hand side of this equation contains nonlinear integro-differential terms responsible for two opposite tendencies: dissipation and swarming. The nonlinear integral operator describes the changes of velocities (orientations) of interacting individuals. The interaction rate is assumed to be dependent of velocities of interacting individuals. Although the equation seems to be rather simple it leads to very complicated dynamics. In this paper, we study possible blow-ups versus global existence of solutions and provide results on the asymptotic behavior. The complicated dynamics and possibility of blow-ups can be directly related to creation of swarms.

scholarly journals The Muskat problem with surface tension and equal viscosities in subcritical $$L_p$$-Sobolev spaces

2021 ◽  
Author(s):  
Anca-Voichita Matioc ◽  
Bogdan-Vasile Matioc
Keyword(s):  
Mathematical Model ◽  
Surface Tension ◽  
Global Existence ◽  
Sobolev Spaces ◽  
Existence Of Solutions ◽  
Well Posedness ◽  
Global Existence Of Solutions ◽  
Muskat Problem ◽  
The Mathematical Model ◽  
Quasilinear Parabolic

AbstractIn this paper we establish the well-posedness of the Muskat problem with surface tension and equal viscosities in the subcritical Sobolev spaces $$W^s_p(\mathbb {R})$$ W p s ( R ) , where $${p\in (1,2]}$$ p ∈ ( 1 , 2 ] and $${s\in (1+1/p,2)}$$ s ∈ ( 1 + 1 / p , 2 ) . This is achieved by showing that the mathematical model can be formulated as a quasilinear parabolic evolution problem in $$W^{\overline{s}-2}_p(\mathbb {R})$$ W p s ¯ - 2 ( R ) , where $${\overline{s}\in (1+1/p,s)}$$ s ¯ ∈ ( 1 + 1 / p , s ) . Moreover, we prove that the solutions become instantly smooth and we provide a criterion for the global existence of solutions.

scholarly journals Global existence of solutions for a multi-phase flow: A drop in a gas-tube

2016 ◽  
Vol 13 (02) ◽  
pp. 381-415
Author(s):  
Debora Amadori ◽  
Paolo Baiti ◽  
Andrea Corli ◽  
Edda Dal Santo
Keyword(s):  
Global Existence ◽  
Existence Of Solutions ◽  
Inviscid Fluid ◽  
Phase Flow ◽  
Lagrangian Coordinates ◽  
Large Initial Data ◽  
Initial Value ◽  
Global Existence Of Solutions ◽  
Multi Phase Flow ◽  
Multi Phase

In this paper we study the flow of an inviscid fluid composed by three different phases. The model is a simple hyperbolic system of three conservation laws, in Lagrangian coordinates, where the phase interfaces are stationary. Our main result concerns the global existence of weak entropic solutions to the initial-value problem for large initial data.

scholarly journals Global existence of solution for multidimensional generalized double dispersion equation

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Xiaoqiang Dai
Keyword(s):  
Cauchy Problem ◽  
Global Existence ◽  
Dispersion Equation ◽  
Existence Of Solutions ◽  
Existence Of Solution ◽  
New Methods ◽  
Global Existence Of Solutions ◽  
The Cauchy Problem ◽  
Double Dispersion

Abstract In this paper, we study the Cauchy problem of multidimensional generalized double dispersion equation. To prove the global existence of solutions, we introduce some new methods and ideas, and fill some gaps in the established results.

Sign in / Sign up

Export Citation Format

Share Document