scholarly journals Eigenfunction expansion method and the long-time asymptotics for the damped Boussinesq equation

2001 ◽  
Vol 7 (4) ◽  
pp. 675-702 ◽  
Author(s):  
Vladimir Varlamov ◽  
Keyword(s):  
Eigenfunction Expansion ◽  
Boussinesq Equation ◽  
Expansion Method ◽  
Eigenfunction Expansion Method ◽  
Time Asymptotics ◽  
Long Time ◽  
Long Time Asymptotics

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 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

The Quasi-Static Analysis for Two-Dimensional Thin Plates

2011 ◽  
Vol 255-260 ◽  
pp. 166-169
Author(s):  
Li Chen ◽  
Yang Bai
Keyword(s):  
Boundary Conditions ◽  
Eigenfunction Expansion ◽  
Solution Space ◽  
Expansion Method ◽  
Fundamental Solutions ◽  
Thin Plates ◽  
Elastic Plates ◽  
Various Boundary Conditions ◽  
Eigenfunction Expansion Method ◽  
Concentration Phenomena

The eigenfunction expansion method is introduced into the numerical calculations of elastic plates. Based on the variational method, all the fundamental solutions of the governing equations are obtained directly. Using eigenfunction expansion method, various boundary conditions can be conveniently described by the combination of the eigenfunctions due to the completeness of the solution space. The coefficients of the combination are determined by the boundary conditions. In the numerical example, the stress concentration phenomena produced by the restriction of displacement conditions is discussed in detail.

Sign in / Sign up

Export Citation Format

Share Document