Nonlocal Estimates of First Derivatives of the Solutions of the Initial Boundary Problem for Nonuniformly Elliptic and Nonuniformly Parabolic Nondivergent Equations

Author(s):  
N. M. Ivochkina ◽  
A. P. Oskolkov
Symmetry ◽  
2019 ◽  
Vol 11 (1) ◽  
pp. 73
Author(s):  
Djumaklich Amanov ◽  
Gafurjan Ibragimov ◽  
Adem Kılıçman

In the present paper, we study a generalization of the initial-boundary problem for the inhomogeneous vibrating string equation. The initial conditions include the higher order derivatives of the unknown function. The problem is studied under homogeneous boundary conditions of the first kind. The uniqueness and existence of a regular solution of the problem are proved. To prove the main result we use the spectral decomposition method.


2021 ◽  
Vol 2131 (3) ◽  
pp. 032091
Author(s):  
A M Slidenko ◽  
V M Slidenko ◽  
S G Valyukhov

Abstract There have been examined the mathematic model of the impact device provided for geological materials destruction. Basic elements of the impact device are variable cross-section tool, striker and impact device body. The interaction of these elements is described as a movement of two discrete mass and the rod in the presence of rigid and dissipative connections. One equation in partial derivatives and two ordinary differential equations associated by initial and boundary conditions represent the initial-boundary problem. The numerical method parameters of which are determined at tests problems solution by Fourier method is used for looking for solutions of mixed initial-boundary problem. Researches are made, and parameters determining the damping efficiency of tool, striker and impact device body oscillations are evaluated.


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