Institute of Mathematics

References:
[1] R. A. Adams: Anisotropic Sobolev inequalities. Čas. pěstování mat. 113 (1988), 267-279. DOI 10.21136/CPM.1988.108786 | MR 960763 | Zbl 0663.46024
[2] Y. Ahakkoud, J. Bennouna, M. Elmassoudi: Existence of a renormalized solutions to a nonlinear system in Orlicz spaces. Filomat 36 (2022), 5073-5092. DOI 10.2298/FIL2215073A | MR 4554393
[3] S. N. Antontsev, M. Chipot: The thermistor problem: Existence, smoothness, uniqueness, blowup. SIAM J. Math. Anal. 25 (1994), 1128-1156. DOI 10.1137/S0036141092233482 | MR 1278895 | Zbl 0808.35059
[4] M. Badii: On the existence of periodic solutions in the thermistor problem with degenerate thermal conductivity. Ann. Univ. Ferrara, Sez. VII, Sci. Mat. 52 (2006), 53-64. DOI 10.1007/s11565-006-0005-6 | MR 2246905 | Zbl 1107.35311
[5] M. Bahari, R. El Arabi, M. Rhoudaf: Capacity solution for a perturbed nonlinear coupled system. Ric. Mat. 69 (2020), 215-233. DOI 10.1007/s11587-019-00459-7 | MR 4098182 | Zbl 1439.35138
[6] N. Benaichouche, H. Ayadi, F. Mokhtari: The anisotropic thermistor problem with degenerate thermal and electric conductivities. J. Elliptic Parabol. Equ. 9 (2023), 901-918. DOI 10.1007/s41808-023-00229-5 | MR 4655045 | Zbl 1526.35151
[7] O. Blasco, S. Pérez-Esteva: The Bergman projection on weighted spaces: $L^1$ and Herz spaces. Stud. Math. 150 (2002), 151-162. DOI 10.4064/sm150-2-4 | MR 1892726 | Zbl 1008.47035
[8] M. Chipot, G. Cimatti: A uniqueness result for the thermistor problem. Eur. J. Appl. Math. 2 (1991), 97-103. DOI 10.1017/S0956792500000425 | MR 1117816 | Zbl 0751.35022
[9] L. Diening, P. Harjulehto, P. Hästö, M. Růžička: Lebesgue and Sobolev Spaces with Variable Exponents. Lecture Notes in Mathematics 2017. Springer, Berlin (2011). DOI 10.1007/978-3-642-18363-8 | MR 2790542 | Zbl 1222.46002
[10] F. G. Düzgün, S. Mosconi, V. Vespri: Anisotropic Sobolev embeddings and the speed of propagation for parabolic equations. J. Evol. Equ. 19 (2019), 845-882. DOI 10.1007/s00028-019-00493-w | MR 3997246 | Zbl 1423.35145
[11] X. Fan: Anisotropic variable exponent Sobolev spaces and $\overrightarrow{p}(x)$-Laplacian equations. Complex Var. Elliptic Equ. 56 (2011), 623-642. DOI 10.1080/17476931003728412 | MR 2832206 | Zbl 1236.46029
[12] X. Fan, J. Shen, D. Zhao: Sobolev embedding theorems for spaces $W^{k,p(x)}(\Omega)$. J. Math. Anal. Appl. 262 (2001), 749-760. DOI 10.1006/jmaa.2001.7618 | MR 1859337 | Zbl 0995.46023
[13] M. T. González Montesinos, F. Ortegón Gallego: The evolution thermistor problem with degenerate thermal conductivity. Commun. Pure Appl. Anal. 1 (2002), 313-325. DOI 10.3934/cpaa.2002.1.313 | MR 1903000 | Zbl 1012.35047
[14] M. T. González Montesinos, F. Ortegón Gallego: Existence of a capacity solution to a coupled nonlinear parabolic-elliptic system. Commun. Pure Appl. Anal. 6 (2007), 23-42. DOI 10.3934/cpaa.2007.6.23 | MR 2276328 | Zbl 1141.35352
[15] M. T. González Montesinos, F. Ortegón Gallego: The evolution thermistor problem under the Wiedemann-Franz law with metallic conduction. Discrete Contin. Dyn. Syst., Ser. B 8 (2007), 901-923. DOI 10.3934/dcdsb.2007.8.901 | MR 2342128 | Zbl 1142.35450
[16] M. T. González Montesinos, F. Ortegón Gallego: The thermistor problem with degenerate thermal conductivity and metallic conduction. Discrete Contin. Dyn. Syst. 2007 (2007), 446-455. DOI 10.3934/proc.2007.2007.446 | MR 2409880 | Zbl 1163.35442
[17] P. Guan, J. Fan: Global existence, uniqueness, and asymptotic behavior of the solutions of the thermistor problem. J. Nanjing Univ., Math. Biq. 13 (1996), 156-167. MR 1440100 | Zbl 0884.35024
[18] E. Guariglia, R. C. Guido: Chebyshev wavelet analysis. J. Funct. Spaces 2022 (2022), Article ID 5542054, 17 pages. DOI 10.1155/2022/5542054 | MR 4456105
[19] E. Guariglia, S. Silvestrov: Fractional-wavelet analysis of positive definite distributions and wavelets on $\mathcal{D}'(\Bbb{C})$. Engineering Mathematics. II. Algebraic, Stochastic and Analysis Structures for Networks, Data Classification and Optimization. Springer, Cham (2016), 337-353. DOI 10.1007/978-3-319-42105-6_16 | MR 3630586 | Zbl 1365.65294
[20] V. S. Guliyev, M. N. Omarova, M. A. Ragusa: Characterizations for the genuine Calderón-Zygmund operators and commutators on generalized Orlicz-Morrey spaces. Adv. Nonlinear Anal. 12 (2023), Article ID 20220307, 16 pages. DOI 10.1515/anona-2022-0307 | MR 4626319 | Zbl 1530.42026
[21] H. Khelifi: Existence and regularity for solution to a degenerate problem with singular gradient lower order term. Moroccan J. Pure Appl. Anal. 8 (2022), 310-327. DOI 10.2478/mjpaa-2022-0022 | Zbl 1549.35233
[22] H. Khelifi: The obstacle problem for nonlinear degenerate elliptic equations with variable exponents and $L^1$-data. J. Partial Diff. Equations 35 (2022), 101-122. DOI 10.4208/jpde.v35.n2.1 | MR 4417495 | Zbl 1499.35294
[23] H. Khelifi: Application of the Stampacchia lemma to anisotropic degenerate elliptic equations. J. Innov. Appl. Math. Comput. Sci. 3 (2023), 75-82. DOI 10.58205/jiamcs.v3i1.68
[24] H. Khelifi: Anisotropic degenerate elliptic problem with singular gradient lower order term. Boll. Unione Mat. Ital. 17 (2024), 149-174. DOI 10.1007/s40574-023-00395-3 | MR 4703444 | Zbl 1533.35153
[25] H. Khelifi: Anisotropic parabolic-elliptic systems with degenerate thermal conductivity. Appl. Anal. 103 (2024), 2069-2101. DOI 10.1080/00036811.2023.2282140 | MR 4774280 | Zbl 1548.35109
[26] H. Khelifi, F. Mokhtari: Nonlinear degenerate anisotropic elliptic equations with variable exponents and $L^1$ data. J. Partial Differ. Equations 33 (2020), 1-16. DOI 10.4208/jpde.v33.n1.1 | MR 4218038 | Zbl 1463.35252
[27] H. Khelifi, M. A. Zouatini: Nonlinear degenerate $p(x)$-Laplacian equation with singular gradient and lower order term. Indian J. Pure Appl. Math. 56 (2025), 46-66. DOI 10.1007/s13226-023-00460-9 | MR 4858041 | Zbl 07985479
[28] O. Kováčik, J. Rákosník: On spaces $L^{p(x)}$ and $W^{k,p(x)}$. Czech. Math. J. 41 (1991), 592-618. DOI 10.21136/CMJ.1991.102493 | MR 1134951 | Zbl 0784.46029
[29] S. N. Kruzhkov, I. M. Kolodij: On the theory of embedding of anisotropic Sobolev spaces. Russ. Math. Surv. 38 (1983), 188-189. DOI 10.1070/RM1983v038n02ABEH003476 | MR 0695478 | Zbl 0534.46022
[30] H. Le Dret: Nonlinear Elliptic Partial Differential Equations: An Introduction. Universitext. Springer, Cham (2018). DOI 10.1007/978-3-319-78390-1 | MR 3793605 | Zbl 1405.35001
[31] G. Li, G. Wang, L. Zhang: A capacity associated with the weighted Lebesgue space and its applications. J. Funct. Spaces 2022 (2022), Article ID 1257963, 11 pages. DOI 10.1155/2022/1257963 | MR 4392088 | Zbl 1495.46021
[32] J. L. Lions: Quelques méthodes de résolution des problèmes aux limites non linéaires. Dunod, Paris (1969). (In French.) MR 0259693 | Zbl 0189.40603
[33] N. Mokhtar: Anisotropic nonlinear elliptic systems with variable exponents, degenerate coercivity and $L^{q(\cdot)}$ data. Ann. Acad. Rom. Sci., Math. Appl. 14 (2022), 107-140. DOI 10.56082/annalsarscimath.2022.1-2.107 | MR 4419207 | Zbl 1513.35243
[34] H. Moussa, F. Ortegón Gallego, M. Rhoudaf: Capacity solution to a coupled system of parabolic-elliptic equations in Orlicz-Sobolev spaces. NoDEA, Nonlinear Differ. Equ. Appl. 25 (2018), Article ID 14, 37 pages. DOI 10.1007/s00030-018-0505-y | MR 3773787 | Zbl 1391.35233
[35] R. Nesraoui, H. Khelifi: Anisotropic elliptic problem involving a singularity and a Radon measure. Filomat 38 (2024), 9435-9451. DOI 10.2298/FIL2427435N | MR 4853204
[36] S. M. Nikol'skij: Imbedding theorems for functions with partial derivatives, considered in different metrics. Dokl. Akad. Nauk SSSR 118 (1958), 35-37. (In Russian.) MR 0093561 | Zbl 0206.12205
[37] F. Ortegón Gallego, M. Rhoudaf, H. Talbi: Capacity solution and numerical approximation to a nonlinear coupled elliptic system in anisotropic Sobolev spaces. J. Appl. Anal. Comput. 12 (2022), 2184-2207. DOI 10.11948/20210208 | MR 4512852 | Zbl 07919237
[38] H. Rafeiro, S. Samko: Riesz potential operator in continual variable exponents Herz spaces. Math. Nachr. 288 (2015), 465-475. DOI 10.1002/mana.201300270 | MR 3320460 | Zbl 1325.46034
[39] M. A. Ragusa: Parabolic Herz spaces and their applications. Appl. Math. Lett. 25 (2012), 1270-1273. DOI 10.1016/j.aml.2011.11.022 | MR 2947392 | Zbl 1255.35131
[40] J. Rákosník: Some remarks to anisotropic Sobolev spaces. I. Beitr. Anal. 13 (1979), 55-68. MR 0536217 | Zbl 0399.46025
[41] J. Rákosník: Some remarks to anisotropic Sobolev spaces. II. Beitr. Anal. 15 (1981), 127-140. MR 0614784 | Zbl 0494.46034
[42] M. Troisi: Teoremi di inclusione per spazi di Sobolev non isotropi. Ric. Mat. 18 (1969), 3-24. (In Italian.) MR 0415302 | Zbl 0182.16802
[43] W. Xie: On the existence and uniqueness for the thermistor problem. Adv. Math. Sci. Appl. 2 (1993), 63-73. MR 1239249 | Zbl 0808.35154
[44] X. Xu: A degenerate Stefan-like problem with Joule's heating. SIAM J. Math. Anal. 23 (1992), 1417-1438. DOI 10.1137/0523081 | MR 1185636 | Zbl 0768.35081
[45] X. Xu: A strongly degenerate system involving an equation of parabolic type and an equation of elliptic type. Commun. Partial Differ. Equations 18 (1993), 199-213. DOI 10.1080/03605309308820927 | MR 1211731 | Zbl 0814.35062
[46] X. Xu: On the existence of bounded temperature in the thermistor problem with degeneracy. Nonlinear Anal., Theory Methods Appl., Ser. A 42 (2000), 199-213. DOI 10.1016/S0362-546X(98)00340-X | MR 1773978 | Zbl 0964.35005
[47] G. Yuan, Z. Liu: Existence and uniqueness of the $C^{\alpha}$ solution for the thermistor problem with mixed boundary value. SIAM J. Math. Anal. 25 (1994), 1157-1166. DOI 10.1137/S0036141092237893 | MR 1278896 | Zbl 0808.35064
[48] X. Zhang, Y. Fu: Solutions for nonlinear elliptic equations with variable growth and degenerate coercivity. Ann. Mat. Pura Appl. (4) 193 (2014), 133-161. DOI 10.1007/s10231-012-0270-1 | MR 3158842 | Zbl 1305.35063
[49] M. A. Zouatini, H. Khelifi, F. Mokhtari: Anisotropic degenerate elliptic problem with a singular nonlinearity. Adv. Oper. Theory 8 (2023), Article ID 13, 24 pages. DOI 10.1007/s43036-022-00240-y | MR 4530493 | Zbl 1506.35078
[50] M. A. Zouatini, F. Mokhtari, H. Khelifi: Degenerate elliptic problem with singular gradient lower order term and variable exponents. Math. Model. Comput. 10 (2023), 133-146. DOI 10.23939/mmc2023.01.133