Geodesic
On some linear two-dimensional Volterra integral equations of the first kind
Sibirskij žurnal industrialʹnoj matematiki, Tome 27 (2024) no. 2, pp. 112-120 Cet article a éte moissonné depuis la source Math-Net.Ru

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The problem of identifying Volterra kernels is an important stage in the construction of integral models of nonlinear dynamical systems based on the tool of Volterra series. The paper considers a new class of two-dimensional integral equations that arise when recovering nonsymmetric kernels in a Volterra polynomial of the second degree, where $x(t)$ is the input vector function of time. The strategy for choosing test signals used to solve this problem is based on applying piecewise linear functions (with a rising edge). An explicit inversion formula is constructed for the selected type of Volterra equations of the first kind with variable integration limits. The questions of existence and uniqueness of solutions of the corresponding equations in the class $C_{[0,T]}$ are studied.
Keywords: two-dimensional Volterra integral equation of the first kind
Mots-clés : identification, inversion formula. 
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S. V. Solodusha. On some linear two-dimensional Volterra integral equations of the first kind. Sibirskij žurnal industrialʹnoj matematiki, Tome 27 (2024) no. 2, pp. 112-120. http://geodesic.mathdoc.fr/item/SJIM_2024_27_2_a7/

[1] V. M. Glushkov, “On one class of dynamic macroeconomic models”, Upr. Sist. Mash., 1977, no. 2, 3–6 (in Russian)

[2] I. V. Boikov and A. N. Tynda, “Approximate solution of nonlinear integral equations of the theory of developing systems”, Differ. Equations, 39:9 (2003), 1277–1288 | DOI

[3] Markova E. V., Sidler I. V., “Numerical solution of the age structure optimization problem for basic types of power plants”, Yugosl. J. Oper. Res., 29:1 (2019), 81–92 | DOI

[4] A. S. Apartsin, “On Volterra integral equations of the first kind in the theory of developing systems”, Numerical Methods of Optimization and Analysis, 1992, 58–67

[5] A. S. Apartsin, Nonclassical Volterra Equations of the First Kind. Theory and Numerical Methods, Nauka, Novosibirsk, 1999

[6] V. F. Volkodavov and I. N. Rodionova, “Inversion formulas for some two-dimensional Volterra integral equations of the first kind”, Russ. Math., 42:9 (1998), 28–30

[7] M. N. Botoroeva and M. V. Bulatov, “Applications and methods of numerical solution of one class of integro-algebraic equations with variable integration limits”, Izv. IGU Ser. Mat., 20 (2017), 3–16 (in Russian) | DOI

[8] A. A. Asanov and S. M. Choyubekov, “Solution of non-classical Volterra integral equations of the first kind with a degenerate nonlinear kernel”, Mezhdunar. Nauchn.-Issled. Zh., 2018, no. 4(70), 134–138 (in Russian) | DOI

[9] V. Volterra, Theory of Functionals and of Integral and Integro-Differential Equations, Dover, New York, 1959

[10] S. V. Solodusha, “On a new class of two-dimensional integral equations of the first kind of Volterra type with variable limits of integration”, Tr. IMM UrO RAN, 28, no. 4, 2022, 216–225 | DOI

[11] Solodusha S. V., “Identification of Symmetric Volterra Kernels Using Piecewise Linear Test Signals”, Proc. 16th Int. Conf. Stab. Oscil. Nonlinear Control Syst., 2022 | DOI

[12] A. S. Apartsin, Theorems of the existence and uniqueness of solutions of Volterra equations of the first kind related to the identification of nonlinear dynamic systems (vector case), Preprint of SEI SO RAN, No 8, Irkutsk, 1996 (in Russian)