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Applied Sciences
Volume 16
Issue 1
10.3390/app16010451
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Article

Some Technical Aspects for the Solution of Initial-Value Problem in Linear Thermodiffusion in the Thermal Stresses Theory with Application in Mechanical Engineering

by
Jerzy Gawinecki
1,
Stanisław Kachel
1,
Adam Kozakiewicz
1,
Łukasz Kiszkowiak
1,*,
Konrad Wojtowicz
1,
Cristian-Emil Moldoveanu
2 and
Michał Ciałkowski
3
1
Faculty of Mechatronics, Armament and Aerospace, Military University of Technology, Kaliskiego 2, 00-908 Warsaw, Poland
2
Faculty of Integrated Armament Systems, Military Engineering and Mechatronics, Military Technical Academy “Ferdinand I”, 39-49 George Cosbuc Avenue, 050141 Bucharest, Romania
3
Faculty of Environmental Engineering and Energy, Poznan University of Technology, 5 M. Skłodowska-Curie Square, 60-965 Poznan, Poland
*
Author to whom correspondence should be addressed.
Appl. Sci. 2026, 16(1), 451; https://doi.org/10.3390/app16010451
Submission received: 17 September 2025 / Revised: 18 December 2025 / Accepted: 22 December 2025 / Published: 31 December 2025
Versions Notes

Abstract

In this paper, we consider the solution of the initial-value problem in thermodiffusion in a solid body in three-dimensional space. Not only do we prove the behavior of the solution over time, but we identify some of its technical aspects as well. Stabilizing a thermodiffusion system in solids is essential for understanding the long-time behaviour of some materials, which are used in mechanical engineering; this is especially important for materials used in aviation, not only in civil aviation but in the air force as well.
Keywords: thermodiffusion; thermal stresses theory; hyperbolic-parabolic partial; differential equations; Lp-Lq time decay; mechanical engineering thermodiffusion; thermal stresses theory; hyperbolic-parabolic partial; differential equations; Lp-Lq time decay; mechanical engineering

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MDPI and ACS Style

Gawinecki, J.; Kachel, S.; Kozakiewicz, A.; Kiszkowiak, Ł.; Wojtowicz, K.; Moldoveanu, C.-E.; Ciałkowski, M. Some Technical Aspects for the Solution of Initial-Value Problem in Linear Thermodiffusion in the Thermal Stresses Theory with Application in Mechanical Engineering. Appl. Sci. 2026, 16, 451. https://doi.org/10.3390/app16010451

AMA Style

Gawinecki J, Kachel S, Kozakiewicz A, Kiszkowiak Ł, Wojtowicz K, Moldoveanu C-E, Ciałkowski M. Some Technical Aspects for the Solution of Initial-Value Problem in Linear Thermodiffusion in the Thermal Stresses Theory with Application in Mechanical Engineering. Applied Sciences. 2026; 16(1):451. https://doi.org/10.3390/app16010451

Chicago/Turabian Style

Gawinecki, Jerzy, Stanisław Kachel, Adam Kozakiewicz, Łukasz Kiszkowiak, Konrad Wojtowicz, Cristian-Emil Moldoveanu, and Michał Ciałkowski. 2026. "Some Technical Aspects for the Solution of Initial-Value Problem in Linear Thermodiffusion in the Thermal Stresses Theory with Application in Mechanical Engineering" Applied Sciences 16, no. 1: 451. https://doi.org/10.3390/app16010451

APA Style

Gawinecki, J., Kachel, S., Kozakiewicz, A., Kiszkowiak, Ł., Wojtowicz, K., Moldoveanu, C.-E., & Ciałkowski, M. (2026). Some Technical Aspects for the Solution of Initial-Value Problem in Linear Thermodiffusion in the Thermal Stresses Theory with Application in Mechanical Engineering. Applied Sciences, 16(1), 451. https://doi.org/10.3390/app16010451

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