Generalized Solutions of Abstract Stochastic Problems

2013 ◽  
pp. 341-352
Author(s):  
I. V. Melnikova ◽  
M. A. Alshanskiy
Keyword(s):  
Generalized Solutions ◽  
Stochastic Problems

Regularized and generalized solutions of infinite-dimensional stochastic problems

2011 ◽  
Vol 202 (11) ◽  
pp. 1565-1592 ◽  
Author(s):  
Maxim A Alshanskiy ◽  
Irina V Mel'nikova
Keyword(s):  
Generalized Solutions ◽  
Infinite Dimensional ◽  
Stochastic Problems

Generalized solutions to abstract stochastic problems

2009 ◽  
Vol 20 (3-4) ◽  
pp. 199-206 ◽  
Author(s):  
Irina V. Melnikova ◽  
Alexei Filinkov
Keyword(s):  
Generalized Solutions ◽  
Stochastic Problems

BENDING OF A SUBTLE-FINISHED PLATE ON ELASTIC BASE WITH SPECIAL CONDITIONS OF ITS WORK

2019 ◽  
pp. 424-430
Author(s):  
A. T. Marufiy ◽  
A. S. Kalykov
Keyword(s):  
Analytical Solution ◽  
Working Conditions ◽  
Fourier Transforms ◽  
Infinite Plate ◽  
Elastic Base ◽  
Generalized Solutions ◽  
Middle Plane ◽  
Actual Working

In this article, an analytical solution is obtained for the problem of bending a semi-infinite plate on an elastic Winkler base, taking into account incomplete contact with the base and the influence of longitudinal forces applied in the middle plane of the plate. The analytical solution is obtained by the method of generalized solutions using integral Fourier transforms. Any analytical solution is the result, approaching the actual working conditions of the designed structures.

scholarly journals GENERALIZED SOLUTIONS FOR THE EULER–BERNOULLI MODEL WITH ZENER VISCOELASTIC FOUNDATIONS AND DISTRIBUTIONAL FORCES

2013 ◽  
Vol 11 (02) ◽  
pp. 1350017 ◽  
Author(s):  
GÜNTHER HÖRMANN ◽  
SANJA KONJIK ◽  
LJUBICA OPARNICA
Keyword(s):  
Differential Equation ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Variational Problems ◽  
Generalized Solutions ◽  
Beam Model ◽  
Order Partial Differential Equation ◽  
Viscoelastic Foundation ◽  
Regularization Techniques ◽  
Initial Boundary Value

We study the initial-boundary value problem for an Euler–Bernoulli beam model with discontinuous bending stiffness laying on a viscoelastic foundation and subjected to an axial force and an external load both of Dirac-type. The corresponding model equation is a fourth-order partial differential equation and involves discontinuous and distributional coefficients as well as a distributional right-hand side. Moreover the viscoelastic foundation is of Zener-type and described by a fractional differential equation with respect to time. We show how functional analytic methods for abstract variational problems can be applied in combination with regularization techniques to prove existence and uniqueness of generalized solutions.

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