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Abstract

We propose a numerical surface integral method to study complex acoustic systems, for interior and exterior problems. The method is based on a parametric representation in terms of the arc’s lengths in curvilinear orthogonal coordinates. With this method, any geometry that involves quadric or higher order surfaces, irregular objects or even randomly rough surfaces can be considered. In order to validate the method, the modes in cubic, spherical and cylindrical cavities are calculated and compared to analytical results, which produced very good agreement. In addition, as examples, we calculated the scattering in the far field and the near field by an acoustic sphere and a cylindrical structure with a rough cross-section.

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Authors and Affiliations

Juan Antonio Guel-Tapia
Francisco Villa-Villa
Alberto Mendoza-Suarez
Hector Pérez-Aguilar
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Abstract

The control system described by Urysohn type integral equation is considered where the system is nonlinear with respect to the phase vector and is affine with respect to the control vector. The control functions are chosen from the closed ball of the space Lq (Ω; ℝ<sup>m</sup>), q > 1, with radius r and centered at the origin. The trajectory of the system is defined as p-integrable multivariable function from the space Lq (Ω; ℝ<sup>n</sup>), (1/q) + (1/p) = 1, satisfying the system’s equation almost everywhere. It is shown that the system’s trajectories are robust with respect to the fast consumption of the remaining control resource. Applying this result it is proved that every trajectory can be approximated by the trajectory obtained by full consumption of the total control resource.









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Authors and Affiliations

Nesir Huseyin
1
ORCID: ORCID
Anar Huseyin
2
ORCID: ORCID
Khalik G. Guseinov
3
ORCID: ORCID

  1. Department of Mathematics and Science Education, Sivas Cumhuriyet University, 58140 Sivas, Turkey
  2. Department of Statistics and Computer Sciences, Sivas Cumhuriyet University, 58140 Sivas, Turkey
  3. Department of Mathematics, Eskisehir Technical University, 26470 Eskisehir, Turkey
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Abstract

The paper is a newapproach to the Duhamel integral. It contains an overviewof formulas and applications of Duhamel’s integral as well as a number of new results on the Duhamel integral and principle. Basic definitions are recalled and formulas for Duhamel’s integral are derived via Laplace transformation and Leibniz integral rule. Applications of Duhamel’s integral for solving certain types of differential and integral equations are presented. Moreover, an interpretation of Duhamel’s formula in the theory of operator semigroups is given. Some applications of Duhamel’s formula in control systems analysis are discussed. The work is also devoted to the usage of Duhamel’s integral for differential equations with fractional order derivative.
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Bibliography

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Authors and Affiliations

Michał Różański
1
Beata Sikora
1
ORCID: ORCID
Adrian Smuda
1
Roman Wituła
1

  1. Department of Applied Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, Poland

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