On the second boundary value problem for the system of thermoelasticity with microtemperatures

Vita Leonessa; Angelica Malaspina

doi:10.33205/cma.1800066

On the second boundary value problem for the system of thermoelasticity with microtemperatures

Abstract

In this work, we investigate the second BVP (boundary value problem) associated with the linear equilibrium theory of thermoelasticity with microtemperatures. We obtain a solution of the second BVP in terms of a double-layer thermoelastic potential, unlike the results reported in the literature, where a solution is represented by a single-layer thermoelastic potential.

Keywords

Project Number

2022SENJZ3

Thanks

The authors acknowledge the support of the Project funded by the European Union - Next Generation EU under the National Recovery and Resilience Plan (NRRP), Mission 4 Component 2 Investment 1.1 - Call for tender PRIN 2022 No. 104 of February, 2 2022 of Italian Ministry of University and Research; Project code: 2022SENJZ3 (subject area: PE - Physical Sciences and Engineering) “Perturbation problems and asymptotics for elliptic differential equations: variational and potential theoretic methods”.

References

M. Aouadi, M. Ciarletta and F. Passarella: Thermoelastic theory with microtemperatures and dissipative thermodynamics, J. Thermal Stresses, 41 (4) (2018), 522–542.
M. Basheleishvili, L. Bitsadze and G. Jaiani: On fundamental and singular solutions of the system of the plane thermoelasticity with microtemperatures, Bulletin of TICMI, 15 (2011), 5–12.
A. Cialdea: On oblique derivate problem for Laplace equation and connected topics, Rend. Accad. Naz. Sci. XL, Serie 5, Mem. Mat. Parte I, 12 (13) (1988), 181–200.
A. Cialdea, E. Dolce, V. Leonessa and A. Malaspina: New integral representations in the linear theory of viscoelastic materials with voids, Publ. Math. Inst., Nouvelle série, 96 (110) (2014), 49–65.
A. Cialdea, E. Dolce and A. Malaspina: A complement to potential theory in the Cosserat elasticity, Math. Methods Appl. Sci., 38 (3) (2015), 537–547.
A. Cialdea, G.C. Hsiao: Regularization for some boundary integral equations of the first kind in Mechanics, Rend. Accad. Naz. Sci. XL, Serie 5, Mem. Mat. Parte I, 19 (1) (1995), 25–42.
A. Cialdea, V. Leonessa and A. Malaspina: Integral representations for solutions of some BVPs for the Lamé system in multiply connected domains, Bound. Value Probl., 2011 (2011), Article ID: 53.
A. Cialdea, V. Leonessa and A. Malaspina: The Dirichlet Problem for Second-Order Divergence Form Elliptic Operators with Variable Coefficients: The Simple Layer Potential Ansatz, Abstr. Appl. Anal., 2015 (2015), Article ID: 276810.

A. Cialdea , V. Leonessa and A. Malaspina: On the double layer potential ansatz for the n-dimensional Helmholtz equation with Neumann condition, Electron. J. Qual. Theory Differ. Equ., 2020, (2020), Article ID: 71.
A. Cialdea, V. Leonessa and A. Malaspina: On the traction problem for steady elastic oscillations equations: the double layer potential ansatz, Rend. Circ. Mat. Palermo, II. Ser., 72 (3) (2023), 1947–1960.
S. Chirita, M. Ciarletta and C. D’Apice: On the theory of thermoelasticity with microtemperatures, J. Math. Anal. Appl., 397 (1) (2013), 349–361.
M. Dalla Riva, M. Lanza de Cristoforis and P. Musolino: Singularly perturbed boundary value problems–a functional analytic approach, Springer, Cham (2021).
G. Fichera: Una introduzione alla teoria delle equazioni integrali singolari, Rend. Mat., 17 (1958), 82–191.
G. Fichera: Spazi lineari di k-misure e di forme differenziali, in Proc. of Intern. Symposium on Linear Spaces, Jerusalem 1960, Israel Ac. of Sciences and Humanities, Pergamon Press, (1961), 175–226.
H. Flanders: Differential Forms with Applications to the Physical Sciences, Academic Press, New York, San Francisco, London (1963).
S. Gupta, R. Dutta, S. Das and A. K. Verma: Double poromagneto-thermoelastic model with microtemperatures and initial stress under memory-dependent heat transfer, J. Thermal Stresses, 46 (8) (2023), 743–774.
D. Ie¸san: On a theory of micromorphic elastic solids with microtemperatures, J. Thermal Stresses, 24 (2001), 737–752.
D. Ie¸san: On the theory of heat conduction in micromorphic continua, Internat. J. Engrg. Sci., 40 (2002), 1859–1878.
D. Ie¸san: Thermoelasticity of bodies with microstructure and microtemperatures, Internat. J. Solids Structures, 44 (2007), 8648–8662.
D. Iesan, R. Quintanilla: On the Theory of Thermoelasticity with Microtemperatures, J. Thermal Stresses, 23 (2000), 199–215.
D. Ie¸san, R. Quintanilla: On thermoelastic bodies with inner structure and microtemperatures, J. Math. Anal. Appl., 354 (2009), 12–23.
T. Kansal: The Theory of Thermoelasticity with Double Porosity and Microtemperatures, CMST, 28 (3) (2022), 87–107.
V. Leonessa, A. Malaspina: On the Dirichlet Problem for the System of Thermoelasticity with Microtemperatures, Mediterr. J. Math., 22 (2025), Article ID: 95.
L. Liverani, R. Quintanilla: Thermoelasticity with temperature and microtemperatures with fading memory, Math. Mech. Solids, 28 (5) (2022), 1255–1273.
S. G. Mikhlin, S. Prössdorf: Singular integral operators, Springer-Verlag, Berlin (1986).
A. Scalia, M. Svanadze: Potential method in the linear theory of thermoelasticity with microtemperatures, J. Thermal Stresses, 32 (10) (2009), 1024–1042.
A. Scalia, M. Svanadze and R. Tracinà: Basic Theorems in the Equilibrium Theory of Thermoelasticity with Microtemperatures, J. Thermal Stresses, 33 (8) (2010), 721–753.
M. Svanadze: Fundamental solutions of the equations of the theory of thermoelasticity with microtemperatures, J. Thermal Stresses, 27 (2) (2004), 151–170.
M. Svanadze: On the Linear Theory of Thermoelasticity with Microtemperatures, Tech. Mech., 32 (2–5), (2012), 564–576.
M. Svanadze: Potential method in the linear theory of triple porosity thermoelasticity, J. Math. Anal. Appl., 461 (2) (2018), 1585–1605.

Details

Primary Language

English

Subjects

Applied Mathematics (Other)

Journal Section

Research Article

Authors

Vita Leonessa ^*
0000-0001-9547-8397
Italy

Angelica Malaspina
0000-0002-1971-0235
Italy

Early Pub Date

December 16, 2025

Publication Date

December 16, 2025

Submission Date

October 9, 2025

Acceptance Date

December 5, 2025

Published in Issue

Year 2025 Volume: 8 Number: Special Issue: ICCMA

DOI

https://doi.org/10.33205/cma.1800066

IZ

https://izlik.org/JA38JG28EB

Cite

RIS / Bibtex

APA

Leonessa, V., & Malaspina, A. (2025). On the second boundary value problem for the system of thermoelasticity with microtemperatures. Constructive Mathematical Analysis, 8(Special Issue: ICCMA), 57-67. https://doi.org/10.33205/cma.1800066

AMA

1.Leonessa V, Malaspina A. On the second boundary value problem for the system of thermoelasticity with microtemperatures. CMA. 2025;8(Special Issue: ICCMA):57-67. doi:10.33205/cma.1800066

Chicago

Leonessa, Vita, and Angelica Malaspina. 2025. “On the Second Boundary Value Problem for the System of Thermoelasticity With Microtemperatures”. Constructive Mathematical Analysis 8 (Special Issue: ICCMA): 57-67. https://doi.org/10.33205/cma.1800066.

EndNote

Leonessa V, Malaspina A (December 1, 2025) On the second boundary value problem for the system of thermoelasticity with microtemperatures. Constructive Mathematical Analysis 8 Special Issue: ICCMA 57–67.

IEEE

[1]V. Leonessa and A. Malaspina, “On the second boundary value problem for the system of thermoelasticity with microtemperatures”, CMA, vol. 8, no. Special Issue: ICCMA, pp. 57–67, Dec. 2025, doi: 10.33205/cma.1800066.

ISNAD

Leonessa, Vita - Malaspina, Angelica. “On the Second Boundary Value Problem for the System of Thermoelasticity With Microtemperatures”. Constructive Mathematical Analysis 8/Special Issue: ICCMA (December 1, 2025): 57-67. https://doi.org/10.33205/cma.1800066.

JAMA

1.Leonessa V, Malaspina A. On the second boundary value problem for the system of thermoelasticity with microtemperatures. CMA. 2025;8:57–67.

MLA

Leonessa, Vita, and Angelica Malaspina. “On the Second Boundary Value Problem for the System of Thermoelasticity With Microtemperatures”. Constructive Mathematical Analysis, vol. 8, no. Special Issue: ICCMA, Dec. 2025, pp. 57-67, doi:10.33205/cma.1800066.

Vancouver

1.Vita Leonessa, Angelica Malaspina. On the second boundary value problem for the system of thermoelasticity with microtemperatures. CMA. 2025 Dec. 1;8(Special Issue: ICCMA):57-6. doi:10.33205/cma.1800066