A theorem of existence and uniqueness for the quasi-static problem in linear viscoelasticity

1999 ◽  
Vol 2 (2-3) ◽  
pp. 129-142
Author(s):  
Ettore Laserra ◽  
Giovanni Matarazzo
2002 ◽  
Vol 7 (1) ◽  
pp. 93-104 ◽  
Author(s):  
Mifodijus Sapagovas

Numerous and different nonlocal conditions for the solvability of parabolic equations were researched in many articles and reports. The article presented analyzes such conditions imposed, and observes that the existence and uniqueness of the solution of parabolic equation is related mainly to ”smallness” of functions, involved in nonlocal conditions. As a consequence the hypothesis has been made, stating the assumptions on functions in nonlocal conditions are related to numerical algorithms of solving parabolic equations, and not to the parabolic equation itself.


2019 ◽  
Vol 8 (4) ◽  
pp. 36
Author(s):  
Samir H. Abbas

This paper studies the existence and uniqueness solution of fractional integro-differential equation, by using some numerical graphs with successive approximation method of fractional integro –differential equation. The results of written new program in Mat-Lab show that the method is very interested and efficient. Also we extend the results of Butris [3].


2020 ◽  
Vol 91 (5) ◽  
pp. 70-76
Author(s):  
E.V. LEONTIEV ◽  
◽  

The paper considers the system "beam - elastic foundation", in which a beam with free edges was at first on a solid elastic foundation, but when a defect suddenly forms in the foundation under the right side of the beam, part of foundation was removed from design model. As a result of calculations performed by the method of initial parameters, the displacements and internal forces for the static problem are determined. The dynamic problem of determining the forces and displacements was solved, taking into account the three vibration loads F (t) = F sinγt applied at arbitrary points d when the conditions for supporting the right side of the beam on an elastic foundation were changed, the values of the dynamics coefficients were determined. Conditions are formulated that must be taken into account when analyzing the dynamic behavior of a structure under the influence of vibration loads in the case of a change in the conditions of bearing on an elastic foundation.


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