Capacity solutions for a degenerate p i ( x ) -Laplacian thermistor system with electrical conductivities

Hichem Khelifi

Applications of Mathematics (2025)

  • Issue: 2, page 203-230
  • ISSN: 0862-7940

Abstract

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We establish the existence of a capacity solution for a degenerate anisotropic stationary system with variable exponents and electrical conductivity. The system is a generalization of the thermistor problem, addressing the interaction between temperature and electric potential within semiconductor material.

How to cite

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Khelifi, Hichem. "Capacity solutions for a degenerate $p_{i}(x)$-Laplacian thermistor system with electrical conductivities." Applications of Mathematics (2025): 203-230. <http://eudml.org/doc/299975>.

@article{Khelifi2025,
abstract = {We establish the existence of a capacity solution for a degenerate anisotropic stationary system with variable exponents and electrical conductivity. The system is a generalization of the thermistor problem, addressing the interaction between temperature and electric potential within semiconductor material.},
author = {Khelifi, Hichem},
journal = {Applications of Mathematics},
keywords = {degenerate conductivity; anisotropic equation; thermistor problem; variable exponent},
language = {eng},
number = {2},
pages = {203-230},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Capacity solutions for a degenerate $p_\{i\}(x)$-Laplacian thermistor system with electrical conductivities},
url = {http://eudml.org/doc/299975},
year = {2025},
}

TY - JOUR
AU - Khelifi, Hichem
TI - Capacity solutions for a degenerate $p_{i}(x)$-Laplacian thermistor system with electrical conductivities
JO - Applications of Mathematics
PY - 2025
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
IS - 2
SP - 203
EP - 230
AB - We establish the existence of a capacity solution for a degenerate anisotropic stationary system with variable exponents and electrical conductivity. The system is a generalization of the thermistor problem, addressing the interaction between temperature and electric potential within semiconductor material.
LA - eng
KW - degenerate conductivity; anisotropic equation; thermistor problem; variable exponent
UR - http://eudml.org/doc/299975
ER -

References

top
  1. Adams, R. A., 10.21136/CPM.1988.108786, Čas. pěstování mat. 113 (1988), 267-279. (1988) Zbl0663.46024MR960763DOI10.21136/CPM.1988.108786
  2. Ahakkoud, Y., Bennouna, J., Elmassoudi, M., 10.2298/FIL2215073A, Filomat 36 (2022), 5073-5092. (2022) MR4554393DOI10.2298/FIL2215073A
  3. Antontsev, S. N., Chipot, M., 10.1137/S0036141092233482, SIAM J. Math. Anal. 25 (1994), 1128-1156. (1994) Zbl0808.35059MR1278895DOI10.1137/S0036141092233482
  4. Badii, M., 10.1007/s11565-006-0005-6, Ann. Univ. Ferrara, Sez. VII, Sci. Mat. 52 (2006), 53-64. (2006) Zbl1107.35311MR2246905DOI10.1007/s11565-006-0005-6
  5. Bahari, M., Arabi, R. El, Rhoudaf, M., 10.1007/s11587-019-00459-7, Ric. Mat. 69 (2020), 215-233. (2020) Zbl1439.35138MR4098182DOI10.1007/s11587-019-00459-7
  6. Benaichouche, N., Ayadi, H., Mokhtari, F., 10.1007/s41808-023-00229-5, J. Elliptic Parabol. Equ. 9 (2023), 901-918. (2023) Zbl1526.35151MR4655045DOI10.1007/s41808-023-00229-5
  7. Blasco, O., Pérez-Esteva, S., 10.4064/sm150-2-4, Stud. Math. 150 (2002), 151-162. (2002) Zbl1008.47035MR1892726DOI10.4064/sm150-2-4
  8. Chipot, M., Cimatti, G., 10.1017/S0956792500000425, Eur. J. Appl. Math. 2 (1991), 97-103. (1991) Zbl0751.35022MR1117816DOI10.1017/S0956792500000425
  9. Diening, L., Harjulehto, P., Hästö, P., Růžička, M., 10.1007/978-3-642-18363-8, Lecture Notes in Mathematics 2017. Springer, Berlin (2011). (2011) Zbl1222.46002MR2790542DOI10.1007/978-3-642-18363-8
  10. Düzgün, F. G., Mosconi, S., Vespri, V., 10.1007/s00028-019-00493-w, J. Evol. Equ. 19 (2019), 845-882. (2019) Zbl1423.35145MR3997246DOI10.1007/s00028-019-00493-w
  11. Fan, X., 10.1080/17476931003728412, Complex Var. Elliptic Equ. 56 (2011), 623-642. (2011) Zbl1236.46029MR2832206DOI10.1080/17476931003728412
  12. Fan, X., Shen, J., Zhao, D., 10.1006/jmaa.2001.7618, J. Math. Anal. Appl. 262 (2001), 749-760. (2001) Zbl0995.46023MR1859337DOI10.1006/jmaa.2001.7618
  13. Montesinos, M. T. González, Gallego, F. Ortegón, 10.3934/cpaa.2002.1.313, Commun. Pure Appl. Anal. 1 (2002), 313-325. (2002) Zbl1012.35047MR1903000DOI10.3934/cpaa.2002.1.313
  14. Montesinos, M. T. González, Gallego, F. Ortegón, 10.3934/cpaa.2007.6.23, Commun. Pure Appl. Anal. 6 (2007), 23-42. (2007) Zbl1141.35352MR2276328DOI10.3934/cpaa.2007.6.23
  15. Montesinos, M. T. González, Gallego, F. Ortegón, 10.3934/dcdsb.2007.8.901, Discrete Contin. Dyn. Syst., Ser. B 8 (2007), 901-923. (2007) Zbl1142.35450MR2342128DOI10.3934/dcdsb.2007.8.901
  16. Montesinos, M. T. González, Gallego, F. Ortegón, 10.3934/proc.2007.2007.446, Discrete Contin. Dyn. Syst. 2007 (2007), 446-455. (2007) Zbl1163.35442MR2409880DOI10.3934/proc.2007.2007.446
  17. Guan, P., Fan, J., Global existence, uniqueness, and asymptotic behavior of the solutions of the thermistor problem, J. Nanjing Univ., Math. Biq. 13 (1996), 156-167. (1996) Zbl0884.35024MR1440100
  18. Guariglia, E., Guido, R. C., 10.1155/2022/5542054, J. Funct. Spaces 2022 (2022), Article ID 5542054, 17 pages. (2022) MR4456105DOI10.1155/2022/5542054
  19. Guariglia, E., Silvestrov, S., 10.1007/978-3-319-42105-6_16, Engineering Mathematics. II. Algebraic, Stochastic and Analysis Structures for Networks, Data Classification and Optimization Springer, Cham (2016), 337-353. (2016) Zbl1365.65294MR3630586DOI10.1007/978-3-319-42105-6_16
  20. Guliyev, V. S., Omarova, M. N., Ragusa, M. A., 10.1515/anona-2022-0307, Adv. Nonlinear Anal. 12 (2023), Article ID 20220307, 16 pages. (2023) Zbl1530.42026MR4626319DOI10.1515/anona-2022-0307
  21. Khelifi, H., 10.2478/mjpaa-2022-0022, Moroccan J. Pure Appl. Anal. 8 (2022), 310-327. (2022) Zbl1549.35233MR4716415DOI10.2478/mjpaa-2022-0022
  22. Khelifi, H., 10.4208/jpde.v35.n2.1, J. Partial Diff. Equations 35 (2022), 101-122. (2022) Zbl1499.35294MR4417495DOI10.4208/jpde.v35.n2.1
  23. Khelifi, H., 10.58205/jiamcs.v3i1.68, J. Innov. Appl. Math. Comput. Sci. 3 (2023), 75-82. (2023) DOI10.58205/jiamcs.v3i1.68
  24. Khelifi, H., 10.1007/s40574-023-00395-3, Boll. Unione Mat. Ital. 17 (2024), 149-174. (2024) Zbl1533.35153MR4703444DOI10.1007/s40574-023-00395-3
  25. Khelifi, H., 10.1080/00036811.2023.2282140, Appl. Anal. 103 (2024), 2069-2101. (2024) Zbl1548.35109MR4774280DOI10.1080/00036811.2023.2282140
  26. Khelifi, H., Mokhtari, F., 10.4208/jpde.v33.n1.1, J. Partial Differ. Equations 33 (2020), 1-16. (2020) Zbl1463.35252MR4218038DOI10.4208/jpde.v33.n1.1
  27. Khelifi, H., Zouatini, M. A., 10.1007/s13226-023-00460-9, Indian J. Pure Appl. Math. 56 (2025), 46-66. (2025) Zbl07985479MR4858041DOI10.1007/s13226-023-00460-9
  28. Kováčik, O., Rákosník, J., 10.21136/CMJ.1991.102493, Czech. Math. J. 41 (1991), 592-618. (1991) Zbl0784.46029MR1134951DOI10.21136/CMJ.1991.102493
  29. Kruzhkov, S. N., Kolodij, I. M., 10.1070/RM1983v038n02ABEH003476, Russ. Math. Surv. 38 (1983), 188-189. (1983) Zbl0534.46022MR0695478DOI10.1070/RM1983v038n02ABEH003476
  30. Dret, H. Le, 10.1007/978-3-319-78390-1, Universitext. Springer, Cham (2018). (2018) Zbl1405.35001MR3793605DOI10.1007/978-3-319-78390-1
  31. Li, G., Wang, G., Zhang, L., 10.1155/2022/1257963, J. Funct. Spaces 2022 (2022), Article ID 1257963, 11 pages. (2022) Zbl1495.46021MR4392088DOI10.1155/2022/1257963
  32. Lions, J. L., Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Paris (1969), French. (1969) Zbl0189.40603MR0259693
  33. Mokhtar, N., 10.56082/annalsarscimath.2022.1-2.107, Ann. Acad. Rom. Sci., Math. Appl. 14 (2022), 107-140. (2022) Zbl1513.35243MR4419207DOI10.56082/annalsarscimath.2022.1-2.107
  34. Moussa, H., Gallego, F. Ortegón, Rhoudaf, M., 10.1007/s00030-018-0505-y, NoDEA, Nonlinear Differ. Equ. Appl. 25 (2018), Article ID 14, 37 pages. (2018) Zbl1391.35233MR3773787DOI10.1007/s00030-018-0505-y
  35. Nesraoui, R., Khelifi, H., 10.2298/FIL2427435N, Filomat 38 (2024), 9435-9451. (2024) MR4853204DOI10.2298/FIL2427435N
  36. Nikol'skij, S. M., Imbedding theorems for functions with partial derivatives, considered in different metrics, Dokl. Akad. Nauk SSSR 118 (1958), 35-37 Russian. (1958) Zbl0206.12205MR0093561
  37. Gallego, F. Ortegón, Rhoudaf, M., Talbi, H., 10.11948/20210208, J. Appl. Anal. Comput. 12 (2022), 2184-2207. (2022) Zbl07919237MR4512852DOI10.11948/20210208
  38. Rafeiro, H., Samko, S., 10.1002/mana.201300270, Math. Nachr. 288 (2015), 465-475. (2015) Zbl1325.46034MR3320460DOI10.1002/mana.201300270
  39. Ragusa, M. A., 10.1016/j.aml.2011.11.022, Appl. Math. Lett. 25 (2012), 1270-1273. (2012) Zbl1255.35131MR2947392DOI10.1016/j.aml.2011.11.022
  40. Rákosník, J., Some remarks to anisotropic Sobolev spaces. I, Beitr. Anal. 13 (1979), 55-68. (1979) Zbl0399.46025MR0536217
  41. Rákosník, J., Some remarks to anisotropic Sobolev spaces. II, Beitr. Anal. 15 (1981), 127-140. (1981) Zbl0494.46034MR0614784
  42. Troisi, M., Teoremi di inclusione per spazi di Sobolev non isotropi, Ric. Mat. 18 (1969), 3-24 Italian. (1969) Zbl0182.16802MR0415302
  43. Xie, W., On the existence and uniqueness for the thermistor problem, Adv. Math. Sci. Appl. 2 (1993), 63-73. (1993) Zbl0808.35154MR1239249
  44. Xu, X., 10.1137/0523081, SIAM J. Math. Anal. 23 (1992), 1417-1438. (1992) Zbl0768.35081MR1185636DOI10.1137/0523081
  45. Xu, X., 10.1080/03605309308820927, Commun. Partial Differ. Equations 18 (1993), 199-213. (1993) Zbl0814.35062MR1211731DOI10.1080/03605309308820927
  46. Xu, X., 10.1016/S0362-546X(98)00340-X, Nonlinear Anal., Theory Methods Appl., Ser. A 42 (2000), 199-213. (2000) Zbl0964.35005MR1773978DOI10.1016/S0362-546X(98)00340-X
  47. Yuan, G., Liu, Z., 10.1137/S0036141092237893, SIAM J. Math. Anal. 25 (1994), 1157-1166. (1994) Zbl0808.35064MR1278896DOI10.1137/S0036141092237893
  48. Zhang, X., Fu, Y., 10.1007/s10231-012-0270-1, Ann. Mat. Pura Appl. (4) 193 (2014), 133-161. (2014) Zbl1305.35063MR3158842DOI10.1007/s10231-012-0270-1
  49. Zouatini, M. A., Khelifi, H., Mokhtari, F., 10.1007/s43036-022-00240-y, Adv. Oper. Theory 8 (2023), Article ID 13, 24 pages. (2023) Zbl1506.35078MR4530493DOI10.1007/s43036-022-00240-y
  50. Zouatini, M. A., Mokhtari, F., Khelifi, H., 10.23939/mmc2023.01.133, Math. Model. Comput. 10 (2023), 133-146. (2023) MR4703444DOI10.23939/mmc2023.01.133

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