Geodesic
Research into functional equations arising from mathematical modeling of critical states of heterogeneous soft layers
Journal of computational and engineering mathematics, Tome 2 (2015) no. 2, pp. 19-24.

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We obtained the classification of solutions to a functional equation arising from the research into mathematical models of critical states of the plastic layer. The layer is exposed to a tensile stress under conditions of plane deformation. The function of the layer heterogeneity depends presumably on two variables. We demonstrated how the research into the mentioned mathematical models can be reduced to the solution of some nonlinear systems of ordinary differential equations under the conditions of separating the variables for tangent stress and for the heterogeneity function.
Keywords: soft layer, stress state, hypothesis of variables separation, systems of nonlinear differential equations, functional equations. 
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V. L. Dilman; D. A. Trunova. Research into functional equations arising from mathematical modeling of critical states of heterogeneous soft layers. Journal of computational and engineering mathematics, Tome 2 (2015) no. 2, pp. 19-24. http://geodesic.mathdoc.fr/item/JCEM_2015_2_2_a2/

[1] V. L. Dilman, T. V. Eroshkina, Mathematical Modelling of Critical States of the Soft Layers in Heterogeneous Joints, Publishing Center of South Ural State University, Chelyabinsk, 2011

[2] V. L. Dilman, Mathematical Models of the Stress State of Heterogeneous Thin-walled Cylindrical Shells, Publishing Center of South Ural State University, Chelyabinsk, 2007

[3] V. L. Dilman, A. A. Ostsemin, “Stress State and Static Strength of the Plastic Interlayer in Plane Deformation”, Journal of Machinery Manufacture and Reliability, 2005, no. 4, 38–48

[4] V. L. Dilman, A. A. Ostsemin, “On the Stress-deformed State at the Tension of the Plastic Layer with Two Axes of Symmetry”, Mechanics of Solids, 2001, no. 6, 115–124

[5] V. L. Dilman, A. A. Nosachova, “Mathematical Simulation of Critical States of the Plastic Layer”, Tambov University Reports. Series: Natural and Technical Sciences, 18:5-2 (2013), 2502–2504

[6] V. L. Dilman, “The Stress State of the Plastic Layer with Variable Strength Broadwise”, Mechanics of Solids, 2000, no. 1, 141–148

[7] V. L. Dilman, “Investigation of analytical methods of mathematical models of the stress state of thin-walled non-uniform cylindrical shells”, Vestnik of SUSU. Series: Mathematical modeling and programming, 2009, no. 17 (150), 36–58 | Zbl

[8] V. L. Dilman, D. A. Trunova, “Mathematical Modeling of the Critical Sates of a Heterogeneous Plastic Rectangle at Plane Deformation”, Bulletin of the Magnitogorsk State University. Mathematics, 2012, no. 14, 46–55

[9] V. L. Dilman, D. A. Trunova, “Mathematical Modelling of the Critical States of the Heterogeneous Layer Under Different Conditions of Heterogeneity”, Molodoy Issledovatel' - Materialy 66-y Studencheskoy Nauchnoy Konferentsii, Publishing center of SUSU, Chelyabinsk, 2013, 166–171

[10] V. L. Dilman, D. A. Trunova, “The Stress State of a Rectangular Plastic Layer with the Function of Heterogeneity Depending on Two Variables”, Yuzhno-Uralskaya Molodezhnaya Shkola po Matematicheskomu Modelirovaniyu (Chelyabinsk, 29-30 May), Publishing center of SUSU, Chelyabinsk, 2014, 144–151