Well-posedness of initial boundary value problems on longitudinal impact on a composite linear viscoelastic bar

2017 ◽  
Vol 40 (14) ◽  
pp. 5380-5390 ◽  
Author(s):  
Akbar B. Aliev ◽  
Elkhan H. Mammadhasanov
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Initial Boundary ◽  
Longitudinal Impact ◽  
Well Posedness ◽  
Initial Boundary Value Problems ◽  
Linear Viscoelastic ◽  
Initial Boundary Value

scholarly journals Well-posedness for weak and strong solutions of non-homogeneous initial boundary value problems for fractional diffusion equations

2021 ◽  
Vol 24 (1) ◽  
pp. 168-201
Author(s):  
Yavar Kian ◽  
Masahiro Yamamoto
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Strong Solutions ◽  
Initial Boundary ◽  
Fractional Diffusion ◽  
Well Posedness ◽  
Initial Boundary Value Problems ◽  
Fractional Diffusion Equations ◽  
Initial Boundary Value ◽  
Weak And Strong Solutions

Abstract We study the well-posedness for initial boundary value problems associated with time fractional diffusion equations with non-homogenous boundary and initial values. We consider both weak and strong solutions for the problems. For weak solutions, we introduce a definition of solutions which allows to prove the existence of solution to the initial boundary value problems with non-zero initial and boundary values and non-homogeneous source terms lying in some negative-order Sobolev spaces. For strong solutions, we introduce an optimal compatibility condition and prove the existence of the solutions. We introduce also some sharp conditions guaranteeing the existence of solutions with more regularity in time and space.

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.

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