Authors: M. E. KERIMOVA, M. M. SABZALIYEV

Abstract. A boundary value problem stated in an infinite semi-strip for a third order non-classic type differential equation degenerated  into a hyperbolic equation,  is considered. The complete expansion of the solution of the  problem with respect to a small parameter as constructed and the residual term is estimated.

Keywords: boundary value problem, non-classic type differential equation, hyperbolic equation, small parameter, boundary layer type function, residual term

DOI:  https://doi.org/10.32010/j.bmj.2022.14

Authors: A. K. MEKHDIEV, R. K. MEKHTIEV

Abstract. 

An elastic medium is considered, weakened by a doubly periodic system of round holes, filled with absolutely rigid inclusions, soldered along the bypass and has a crack initiation. The medium (binder) is weakened by two periodic systems of rectilinear crack initiation directed collinear to the abscissa and ordinate axes, and their sizes are not the same. General representations are constructed that describe a class of problems with a doubly periodic stress distribution outside circular holes and cracks under transverse shear. The analysis of the limiting equilibrium of cracks in the framework of the end zone model is carried out on the basis of a nonlocal fracture criterion with a force condition for the propagation of the crack tip and a deformation condition for determining the advancement of the edge of the end zone of the crack.

Basic resolving equations are obtained in the form of infinite algebraic systems and three nonlinear singular integro-differential equations.

The equations in each approximation were solved by the Gaussian method with the choice of the principal element for different values of the order of M, depending on the radius of the holes. Calculations were carried out to determine the forces in the connections of the end zones and the ultimate loads causing the growth of cracks.

Keywords: doubly periodic lattice, average stresses, boundary conditions, transverse shear, linear algebraic equations, singular equations, crack initiation

DOI:  https://doi.org/10.32010/j.bmj.2022.13

Authors: N. P. NASIBOVA

Keywords: system of exponents, basicity, variable summability exponent

DOI:  https://doi.org/10.32010/j.bmj.2022.10

COVER and CONTENTS

1. Transverse shear of an isotropic elastic medium in the case when the binder and inclusions are weakened by crack initiation
   A. K. MEKHDIEV, R. K. MEKHTIEV
   Baku Math J, 2022, 1 (2), 125-144
   DOI: https://doi.org/10.32010/j.bmj.2022.13     Full Text: PDF

2. About one boundary value problem for a non-classic type differential equation
   M. E. KERIMOVA, M. M. SABZALIYEV
   Baku Math J, 2022, 1 (2), 145-149
   DOI: https://doi.org/10.32010/j.bmj.2022.14     Full Text: PDF

3. On the asymptotic behavior of solutions of the Sturm-Liouville equation with an oscillating potential
   A. R. SAGITOVA, A. V. SHAKIROVA, Ya. T. SULTANAEV
   Baku Math J, 2022, 1 (2), 150-154
   DOI: https://doi.org/10.32010/j.bmj.2022.15     Full Text: PDF

4. Studying the solution of the system of differential equations obtained in simulation of gas-lift
   process by the relaxation method
   O. Z. NAMAZOV, R. M. TAGIYEV
   Baku Math J, 2022, 1 (2), 155-163
   DOI: https://doi.org/10.32010/j.bmj.2022.16     Full Text: PDF

5. The regularized trace formula for ”weighted” Sturm-Liouville equation with δ-interaction
   A. KARAKUŞ, M. Dzh. MANAFOV
   Baku Math J, 2022, 1 (2), 164-171
   DOI: https://doi.org/10.32010/j.bmj.2022.17     Full Text: PDF

6. Basicity of the systems of sines and cosines with linear phases in grand-Sobolev spaces
   T. R. MURADOV, S. A. NURIEVA, V. F. SALMANOV
   Baku Math J, 2022, 1 (2), 172-178
   DOI: https://doi.org/10.32010/j.bmj.2022.18     Full Text: PDF

7. Inverse Sturm–Liouville problems with polynomials in nonseparated boundary conditions
   A. M. AKHTYAMOV, Kh. R. MAMEDOV, Ya. T. SULTANAEV
   Baku Math J, 2022, 1 (2), 179-194
   DOI: https://doi.org/10.32010/j.bmj.2022.19    Full Text: PDF

8. Inverse boundary value problem for nonlinear diffusion equation with non-local time-integral
   conditions of the second kind
   M. Yu. SALIMOV, A. A. SALIMOVA
   Baku Math J, 2022, 1 (2), 195-204
   DOI: https://doi.org/10.32010/j.bmj.2022.20     Full Text: PDF

9. On the integral representations of solutions of some matrix pencils of the Sturm-Liouville equation
   Sh. T. GURBUZ, A. A. NABIEV, S. SALTAN
   Baku Math J, 2022, 1 (2), 205-229
   DOI: https://doi.org/10.32010/j.bmj.2022.21     Full Text: PDF