scholarly journals Asymptotic behavior of solutions of the damped Boussinesq equation in two space dimensions

1999 ◽  
Vol 22 (1) ◽  
pp. 131-145 ◽  
Author(s):  
Vladimir V. Varlamov
Keyword(s):  
Cauchy Problem ◽  
Existence And Uniqueness ◽  
Boussinesq Equation ◽  
Asymptotic Behavior Of Solutions ◽  
Small Initial Data ◽  
Time Asymptotics ◽  
The Cauchy Problem ◽  
Long Time ◽  
Two Space Dimensions ◽  
Long Time Asymptotics

The Cauchy problem for the damped Boussinesq equation with small initial data is considered in two space dimensions. Existence and uniqueness of its classical solution is proved and the solution is constructed in the form of a series. The major term of its long-time asymptotics is calculated explicitly and a uniform in space estimate of the residual term is given.

scholarly journals Long-time asymptotics of solutions of the second initial-boundary value problem for the damped Boussinesq equation

1997 ◽  
Vol 2 (3-4) ◽  
pp. 281-299 ◽  
Author(s):  
Vladimir V. Varlamov
Keyword(s):  
Boundary Value Problem ◽  
Boussinesq Equation ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Small Initial Data ◽  
Time Asymptotics ◽  
Long Time ◽  
Long Time Asymptotics ◽  
Initial Boundary Value

For the damped Boussinesq equationutt−2butxx=−αuxxxx+uxx+β(u2)xx,x∈(0,π),t>0;α,b=const>0,β=const∈R1, the second initial-boundary value problem is considered with small initial data. Its classical solution is constructed in the form of a series in small parameter present in the initial conditions and the uniqueness of solutions is proved. The long-time asymptotics is obtained in the explicit form and the question of the blow up of the solution in a certain case is examined. The possibility of passing to the limitb→+0in the constructed solution is investigated.

scholarly journals Global existence of strong solutions for incompressible hydrodynamic flow of liquid crystals with vacuum

Filomat ◽  
2013 ◽  
Vol 27 (7) ◽  
pp. 1247-1257 ◽  
Author(s):  
Shijin Ding ◽  
Jinrui Huang ◽  
Fengguang Xia
Keyword(s):  
Cauchy Problem ◽  
Liquid Crystals ◽  
Global Existence ◽  
Existence And Uniqueness ◽  
Strong Solutions ◽  
Hydrodynamic Flow ◽  
Three Dimensions ◽  
Small Initial Data ◽  
The Cauchy Problem ◽  
Global Existence And Uniqueness

We consider the Cauchy problem for incompressible hydrodynamic flow of nematic liquid crystals in three dimensions. We prove the global existence and uniqueness of the strong solutions with nonnegative p0 and small initial data.

scholarly journals Global Existence and Asymptotic Behavior of Solutions to the Generalized Damped Boussinesq Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Yinxia Wang ◽  
Hengjun Zhao
Keyword(s):  
Cauchy Problem ◽  
Asymptotic Behavior ◽  
Global Existence ◽  
Decay Estimate ◽  
Boussinesq Equation ◽  
Asymptotic Behavior Of Solutions ◽  
Initial Value ◽  
Linear Solution ◽  
Optimal Decay ◽  
The Cauchy Problem

We investigate the Cauchy problem for the generalized damped Boussinesq equation. Under small condition on the initial value, we prove the global existence and optimal decay estimate of solutions for all space dimensionsn≥1. Moreover, whenn≥2, we show that the solution can be approximated by the linear solution as time tends to infinity.

scholarly journals Long-time asymptotics for evolutionary crystal dislocation models

2020 ◽  
Vol 371 ◽  
pp. 107242 ◽  
Author(s):  
Matteo Cozzi ◽  
Juan Dávila ◽  
Manuel del Pino
Keyword(s):  
Time Asymptotics ◽  
Dislocation Models ◽  
Long Time ◽  
Long Time Asymptotics
Sign in / Sign up

Export Citation Format

Share Document