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Applicable Analysis
An International Journal
Volume 102, 2023 - Issue 18
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Research Article

Mathematical problems of dynamical interaction of fluids and multiferroic solids

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Pages 5224-5250 | Received 25 Feb 2022, Accepted 17 Jan 2023, Published online: 01 Feb 2023

References

  • Neugschwandtner GS, Schwodiauer R, Bauer-Gogonea S, et al. Piezo- and pyroelectricity of a polymer-foam space-charge electret. J Appl Phys. 2001;89(8):4503–4511.
  • Safari A, Akdogan EK, editors. Piezoelectric and acoustic materials for transducer applications. New York: Springer; 2008.
  • Vopson MM. Fundamentals of multiferroic materials and their possible applications. Crit Rev Solid State Mater Sci. 2015;40(4):223–250.
  • Kupradze VD, Gegelia TG, Basheleishvili MO, et al. Three-dimensional problems of the mathematical theory of elasticity and thermoelasticity. Translated from the second Russian edition. In: Kupradze VD, editor. North-Holland series in applied mathematics and mechanics; 25. Amsterdam-New York: North-Holland Publishing Co; 1979.
  • Natroshvili D, Chkadua O, Shargorodsky E. Mixed problems for homogeneous anisotropic elastic media (in Russian). Tbiliss Gos Univ Inst Prikl Mat Trudy. 1990;39:133–181.
  • Buchukuri T, Gegelia TG. Some dynamic problems of the theory of electroelasticity. Mem Differ Equ Math Phys. 1997;10:1–53.
  • Buchukuri T, Chkadua O, Natroshvili N. Mixed and crack-type dynamical problems of electro-magneto-elasticity theory. Georgian Math J. 2021;28(4):533–553.
  • Hsiao GC, Sánchez-Vizuet T. Time-dependent wave-structure interaction revisited: thermo-piezoelectric scatterers. Fluids. 2021;6(3):101.
  • Hsiao GC, Wendland WL. On the propagation of acoustic waves in a thermo-electro-magneto-elastic solid. Appl Anal. 2022;101(11):3785–3803.
  • Chkadua G, Natroshvili D. Interaction of acoustic waves and piezoelectric structures. Math Meth Appl Sci. 2015;38(11):2149–2170.
  • Chkadua GS. asimptotic analysis and regularity results of mixed type interaction problem of acoustic waves and piezoelectric structures. Math Meth Appl Sci. 2017;40(15):5539–5562.
  • Sánchez-Vizuet T, Sayas FJ. Symmetric boundary-finite element discretization of time dependent acoustic scattering by elastic obstacles with piezoelectric behavior. J Sci Comput. 2017;70(3):1290–1315.
  • Hassell ME, Qiu T, Sánchez-Vizuet T, et al. A new and improved analysis of the time domain boundary integral operators for the acoustic wave equation. J Int Equ Appl. 2017;29(1):107–136.
  • Brown TS, Sánchez-Vizuet T, Sayas FJ. Evolution of a semidiscrete system modeling the scattering of acoustic waves by a piezoelectric solid. ESAIM Math Model Numer Anal. 2018;52(2):423–455.
  • Chkadua G, Natroshvili D. Mathematical aspects of fluid-multiferroic solid interaction problems. Math Meth Appl Sci. 2021;44(12):9727–9745.
  • Straughan B. Heat waves. New York: Springer; 2011. (Applied Mathematical Sciences; vol. 177).
  • Aouadi M. Some theorems in the generalized theory of thermo-magnetoelectroelasticity under Green–Lindsay's model. Acta Mech. 2008;200(1-2):25–43.
  • Green AE, Lindsay KA. Thermoelasticity. J Elast. 1972;2(1):1–7.
  • Buchukuri T, Chkadua O, Natroshvili N. Mathematical problems of generalized thermo-electro-magneto-elasticity theory. Mem Differ Equ Math Phys. 2016;68:1–166.
  • Li JY. Magnetoelectroelastic multi-inclusion and inhomogeneity problems and their applications in composite materials. Int J Eng Sci. 2000;38(18):1993–2011.
  • Li JY. Uniqueness and reciprocity theorems for linear thermo-electro-magneto-elasticity. Quart J Mech Appl Math. 2003;56(1):35–43.
  • Aouadi M. On the coupled theory of thermo-magnetoelectroelasticity. Quart J Mech Appl Math. 2007;60(4):443–456.
  • Novatskiĭ V. Efecty electromagnetyczne w stalych cialach odksztalcalnych. Russian translation: electromagnetic effects in solids. Mechanics: Recent Publications in Foreign Science; 37. Warszawa: Panstwowe Widawnictwo Naukowe; 1983, Moscow: Mir; 1986.
  • Colton D, Kress R. Inverse acoustic and electromagnetic scattering theory. 2nd ed., Berlin: Springer-Verlag; 1998. (Applied Mathematical Sciences; vol. 93).
  • Burchuladze TV, Gegelia TG. Development of the potential method in the theory of elasticity. Tbilisi: Metsniereba; 1985.
  • Zemanian AH. Generalized integral transformations. New York-London-Sydney: Interscience publihser, John Wiley & Sons, Inc.; 1968. (Pure and Applied Mathematics; vol. XVIII).
  • Gel'fand IM, Shilov GE. Generalized functions: properties and operations. Vol. 1, New York-London: Academic Press; 1964.
  • Hardy GH, Littlewood JE, Polya G. Inequalities. London-New York-Toronto: Cambridge University Press; 1934.
  • Chkadua G. Solvebility of mixed type interaction problem of acoustic waves and electro-magneto-elastic structures. Mem Differ Equ Math Phys. 2021;84:69–98.
  • Ciarlet PG, Ciarlet Jr P. Another approach to linearized elasticity and Korn's inequality, mathematical problems in mechanics. C R Acad Sci Paris Ser I. 2004;339(4):307–312.
  • Duvaut G, Lions JL. Inequalities in mechanics and physics. Berlin-Heidelberg-New York: Springer-Verlag; 1976.

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