Vestnik of Samara University. Natural Science Series最新文献

{"title":"Well-posedness of the main mixed problem for the multidimensional Lavrentiev — Bitsadze equation","authors":"S. Aldashev","doi":"10.18287/2541-7525-2021-27-3-7-13","DOIUrl":"https://doi.org/10.18287/2541-7525-2021-27-3-7-13","url":null,"abstract":"It is known that the oscillations of elastic membranes in space are modelled with partial differential equations. If the deflection of the membrane is considered as a function of u(x; t); x = (x1; :::; xm);m 2; then, according to the Hamilton principle, we arrive to a multidimensional wave equation.Assuming that the membrane is in equilibrium in the bending position, we also obtain the multidimensional Laplace equation from the Hamiltons principle.Consequently, the oscillations of elastic membranes in space can be modelled with a multidimensional Lavrentiev Bitsadze equation.The main mixed problem in the cylindrical domain for multidimensional hyperbolic equations in the space of generalized functions is well studied. In the works of the author, the well-posedness of this problem for multidimensional hyperbolic and elliptic equations is proved, and the explicit forms of classical solutions are obtained.As far as we know, these questions for multidimensional hyperbolic-elliptic equations have not been studied.The mixed problem with boundary-value conditions for the multidimensional Lavrentiev Bitsazde equation is ill-posed.In this paper, we prove the unique solvability and obtain an explicit form of classical solution of themain mixed problem with boundary and initial conditions for the multidimensional Lavrentiev Bitsadze equation.","PeriodicalId":427884,"journal":{"name":"Vestnik of Samara University. Natural Science Series","volume":"231 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131091570","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"CHARACTERISTIC PROBLEM FOR A FOURTH-ORDER EQUATION \u0000WITH A DOMINANT DERIVATIVE","authors":"A. Gilev, O. M. Kechina, L. S. Pulkina","doi":"10.18287/2541-7525-2021-27-3-14-21","DOIUrl":"https://doi.org/10.18287/2541-7525-2021-27-3-14-21","url":null,"abstract":"In this article we consider the Goursat problem for an equation with a dominating fourth-order mixed derivative and prove its unique solvability. The equation under consideration can be interpreted as a generalized Boussinesq Love equation, which arises when describing longitudinal waves in a rod, taking into account transverse deformations. To justify the solvability, we proposed a method that is based on the possibility of reducing the problem posed to two Goursat problems for second-order equations. One of the problems is the classical Goursat problem for the simplest hyperbolic equation, while the other equation is loaded, and the study of the Goursat problem for it is the main result of the work.","PeriodicalId":427884,"journal":{"name":"Vestnik of Samara University. Natural Science Series","volume":"4 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"113976312","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"DECOMPOSITION OF TRAVELING WAVES PROBLEMS","authors":"V. Sobolev, E. Tropkina, E. Shchepakina, L. Zhang","doi":"10.18287/2541-7525-2021-27-3-22-30","DOIUrl":"https://doi.org/10.18287/2541-7525-2021-27-3-22-30","url":null,"abstract":"In the article, the traveling waves problem for singularly perturbed systems of semilinear parabolic equations is considered. An effective method for the order reduction of singularly perturbed systems is proposed. The obtained mathematical results are used to study traveling waves both for abstract partial differential equations and for a specific model that can arise in physics problems, chemistry, and biology.","PeriodicalId":427884,"journal":{"name":"Vestnik of Samara University. Natural Science Series","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129321332","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"PROBLEMS OF DIFFERENTIAL AND TOPOLOGICAL DIAGNOSTICS. PART 7. DIFFERENTIAL DIAGNOSTICS IN SOME SYSTEMS OF DIRECT AND INDIRECT CONTROL","authors":"Maxim V. Shamolin","doi":"10.18287/2541-7525-2021-27-3-31-45","DOIUrl":"https://doi.org/10.18287/2541-7525-2021-27-3-31-45","url":null,"abstract":"Proposed work is the seventh work of the cycle on differential and topological diagnostics. Diagnostics ofmalfunctions in the system of indirect control of an object whose motion is described by nonlinear ordinary differential equations of the third order (the problem of B.V. Bulgakov) is considered. In the diagnostic algorithm used, the scope of control is selected, when a certain constant value is assigned to each faulty system, and according to certain rules, the numbers obtained in the process of integrating equations and characterizing the functional state of the system are compared with it. Troubleshooting is also considered in one system of direct control of the movement of the aircraft, which can be described by nonlinear differential equations of the second order. At the same time, a certain diagnostic algorithm is built and used in accordance with the previously developed methodology.","PeriodicalId":427884,"journal":{"name":"Vestnik of Samara University. Natural Science Series","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127838110","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"USE OF THE INDIRECT BOUNDARY ELEMENTS METHOD FOR ISOTROPIC PLATES ON AN ELASTIC WINKLER BASE AND PASTERNAK — VLASOV BASE","authors":"P. Velikanov, N. I. Kukanov, D. Khalitova","doi":"10.18287/2541-7525-2021-27-2-33-47","DOIUrl":"https://doi.org/10.18287/2541-7525-2021-27-2-33-47","url":null,"abstract":"The calculation tasks combining lightness, economy, high strength and reliability of thin-walled structures on an elastic base are relevant for modern mechanical engineering. In this regard, the use of isotropic materials on an elastic base seems justified, therefore their calculation is considered in this article. The problems of the theory of plates and shells belong to the class of boundary value problems, the analytical solution of which, due to various circumstances (the nonlinearity of differential equations, the complexity of geometry and boundary conditions, etc.), cannot be determined. Numerical methods help to solve this problem. Amongnumerical methods, undeservedly little attention is paid to the boundary element method. In this regard, the further development of indirect compensating loads method for solving problems of the theory of isotropic plates on an elastic base of Winkler and Pasternak Vlasov, based on the application of exact fundamentalsolutions, is relevant.","PeriodicalId":427884,"journal":{"name":"Vestnik of Samara University. Natural Science Series","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114755436","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"INFLUENCE OF THE PARAMETERS OF THE BOTTOM BOREHOLE ZONE ON THE OWN VIBRATIONS OF THE LIQUID IN THE PUMP COMPRESSOR TUBING","authors":"G. R. Rafikova, Z. Z. Mamaeva","doi":"10.18287/2541-7525-2021-27-2-70-79","DOIUrl":"https://doi.org/10.18287/2541-7525-2021-27-2-70-79","url":null,"abstract":"The problem of natural oscillations of a liquid column in a tubing string, arising after a sudden opening or closing of a vertical well (water hammer), is considered. For this, a mathematical model has been built that describes the dynamics of the fluid column in the well and the filtration flow in the bottomhole zone, analytical solutions of the system of equations have been obtained. To determine the frequency, period, coefficient and decrement of damping of oscillations, a characteristic equation is found. The impact of such parameters as the length of the open section, the perforation zones of the well, the length of the tubing string, the permeability coefficient on the dynamic nature of natural pressure fluctuations has been analyzed.","PeriodicalId":427884,"journal":{"name":"Vestnik of Samara University. Natural Science Series","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122874055","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"CRITICAL TRAVELLING WAVES IN ONE MODEL OF THE ”REACTION-DIFFUSION” TYPE","authors":"V. Sobolev, E. Tropkina, E. Shchepakina, Lijun Zhang, Jundong Wang","doi":"10.18287/2541-7525-2021-27-2-16-24","DOIUrl":"https://doi.org/10.18287/2541-7525-2021-27-2-16-24","url":null,"abstract":"The paper is devoted to the order reduction for critical traveling wave problems for a reaction-diffusion type systems. The mathematical apparatus is based on the geometric theory of singular perturbations and the canards technique. The use of the method of invariant manifolds of singularly perturbed systems allows us to replace the study of traveling waves of the original PDE system by analyzing their profiles in a ODE system of a lower order.","PeriodicalId":427884,"journal":{"name":"Vestnik of Samara University. Natural Science Series","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125273709","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"ON A CHARACTERISTIC OF STRONGLY EMBEDDED SUBSPACES IN SYMMETRIC SPACES","authors":"S. I. Strakhov","doi":"10.18287/2541-7525-2021-27-2-25-32","DOIUrl":"https://doi.org/10.18287/2541-7525-2021-27-2-25-32","url":null,"abstract":"It is shown that the presence of a lower p - estimate with constant 1 in the symmetric space E is sufficient for the condition of equivalence of convergence in norm and in measure on the subspace H of the space E to be satisfied if and only if the numerical characteristic E(H) 1. The last criterion is also valid for symmetric spaces close to L1, more precisely, for which an analog of the Dunford - Pettis criterion of weak compactness is valid. In particular, it is shown that spaces close to L1, have the binary property: the characteristic E(H) takes only two values, 0 and 1. This gives an example of binary Orlicz spaces differentfrom the spaces Lp.","PeriodicalId":427884,"journal":{"name":"Vestnik of Samara University. Natural Science Series","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129715562","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"INFLUENCE OF CURVATURE OF THE CRACK TIP RADIUS ON STRESSES","authors":"Y. A. Gerber, A. Nagel, M. Tabanyukhova","doi":"10.18287/2541-7525-2021-27-2-62-69","DOIUrl":"https://doi.org/10.18287/2541-7525-2021-27-2-62-69","url":null,"abstract":"In experimental mechanics, when conducting research on models, the question often arises of whether it is legitimate to replace a crack with a cut, whether the radius of curvature of the cut will have a large effect on the magnitude of stresses near its apex. In order to understand these questions and give answers to them, a number of experiments were carried out on samples made of piezo-optical material (Plexiglass of E2 grade). In the models, the crack was simulated using a cut, then a hole was made at the top of the cut with a drill. The models were investigated in pure bending by the photoelasticity method. Stress fields were obtained in two batches of samples at different loads. The intensity of stresses near cracks-cuts at different radius of curvature of their tops was determined by using the experimental data. An assessment ofthe influence of the crack-cut tip radius curvature on the magnitude of stresses near it has been carried out.","PeriodicalId":427884,"journal":{"name":"Vestnik of Samara University. Natural Science Series","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129914308","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"SOLUTIONS OF BOUNDARY VALUE PROBLEMS FOR ANISOTROPIC PLATES AND SHELLS BY BOUNDARY ELEMENTS METHOD","authors":"P. Velikanov, D. Khalitova","doi":"10.18287/2541-7525-2021-27-2-48-61","DOIUrl":"https://doi.org/10.18287/2541-7525-2021-27-2-48-61","url":null,"abstract":"Modern mechanical engineering sets the tasks of calculating thin-walled structures that combine lightness and economy on the one hand and high strength and reliability on the other. In this regard, the use of anisotropic materials and plastics seems justified. The problems of the theory of plates and shells belong to the class of boundary value problems, the analytical solution of which, due to various circumstances (nonlinearity of differential equations, complexity of geometry and boundary conditions, etc.), cannot bedetermined. Numerical methods help to solve this problem. Among numerical methods, undeservedly little attention is paid to the boundary element method. In this regard, the further development of indirect method of compensating loads for solving problems of the anisotropic plates and shells theory based on the applicationof exact fundamental solutions is relevant.The paper considers the application of the indirect boundary element method for solving of an anisotropic plates and shells nonlinear deformation problem. Since the kernels of the system of singular integral equations to which the solution of the problem is reduced are expressed in terms of the fundamental solution and itsderivatives, first of all, the article provides a method for determining the fundamental solutions to the problem of bending and the plane stress state of an anisotropic plate. The displacement vector is determined from the solution of linear equations system describing the bending and plane stress state of an anisotropic plate. The solution of the system is performed by the method of compensating loads, according to which the area representing the plan of the shallow shell is supplemented to an infinite plane, and on the contour that limits the area, compensating loads are applied to the infinite plate. Integral equations of indirect BEM are given. In this paper, the study of nonlinear deformation of anisotropic plates and shallow shells is carried out using the deflection load dependencies. The deflection at a given point on the median surface of the shell was taken as the leading parameter.","PeriodicalId":427884,"journal":{"name":"Vestnik of Samara University. Natural Science Series","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130921749","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}