Asymptotic behavior as t→∞ of the solutions of initial-boundary value problems for the equations of motions of linear viscoelastic fluids

1991 ◽  
Vol 56 (2) ◽  
pp. 2396-2402
Author(s):  
A. P. Oskolkov
Keyword(s):  
Asymptotic Behavior ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Viscoelastic Fluids ◽  
Initial Boundary ◽  
Initial Boundary Value Problems ◽  
Linear Viscoelastic ◽  
Initial Boundary Value ◽  
Equations Of Motions

scholarly journals Solvability of initial boundary value problems for equations describing motions of linear viscoelastic fluids

2005 ◽  
Vol 2005 (1) ◽  
pp. 59-80 ◽  
Author(s):  
N. A. Karazeeva
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Strain Tensor ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Initial Boundary Value Problems ◽  
Additional Hypothesis ◽  
Definite Operator ◽  
Linear Viscoelastic ◽  
Initial Boundary Value

The nonlinear parabolic equations describing motion of incompressible media are investigated. The rheological equations of most general type are considered. The deviator of the stress tensor is expressed as a nonlinear continuous positive definite operator applied to the rate of strain tensor. The global-in-time estimate of solution of initial boundary value problem is obtained. This estimate is valid for systems of equations of any non-Newtonian fluid. Solvability of initial boundary value problems for such equations is proved under some additional hypothesis. The application of this theory makes it possible to prove the existence of global-in-time solutions of two-dimensional initial boundary value problems for generalized linear viscoelastic liquids, that is, for liquids with linear integral rheological equation, and for third-grade liquids.

Asymptotic estimates of solutions to initial-boundary-value problems for distributed order time-fractional diffusion equations

2014 ◽  
Vol 17 (4) ◽  
Author(s):  
Zhiyuan Li ◽  
Yuri Luchko ◽  
Masahiro Yamamoto
Keyword(s):  
Asymptotic Behavior ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Initial Boundary ◽  
Fractional Diffusion ◽  
Diffusion Equations ◽  
Initial Boundary Value Problems ◽  
Fractional Diffusion Equations ◽  
Initial Boundary Value ◽  
Distributed Order

AbstractThis article deals with investigation of some important properties of solutions to initial-boundary-value problems for distributed order time-fractional diffusion equations in bounded multi-dimensional domains. In particular, we investigate the asymptotic behavior of the solutions as the time variable t → 0 and t → +∞. By the Laplace transform method, we show that the solutions decay logarithmically as t → +∞. As t → 0, the decay rate of the solutions is dominated by the term (t log(1/t))−1. Thus the asymptotic behavior of solutions to the initial-boundary-value problem for the distributed order time-fractional diffusion equations is shown to be different compared to the case of the multi-term fractional diffusion equations.

Sign in / Sign up

Export Citation Format

Share Document