Title:
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Existence results for some nonlinear parabolic equations with degenerate coercivity and singular lower-order terms (English) |
Author:
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Mecheter, Rabah |
Author:
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Mokhtari, Fares |
Language:
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English |
Journal:
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Mathematica Bohemica |
ISSN:
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0862-7959 (print) |
ISSN:
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2464-7136 (online) |
Volume:
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148 |
Issue:
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4 |
Year:
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2023 |
Pages:
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561-581 |
Summary lang:
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English |
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Category:
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math |
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Summary:
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In this paper, we study the existence results for some parabolic equations with degenerate coercivity, singular lower order term depending on the gradient, and positive initial data in $L^1$. (English) |
Keyword:
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singular equation |
Keyword:
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nonlinear parabolic equation |
Keyword:
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degenerate coercivity |
MSC:
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35K55 |
MSC:
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35K65 |
MSC:
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35K67 |
DOI:
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10.21136/MB.2022.0152-21 |
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Date available:
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2023-11-23T12:39:25Z |
Last updated:
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2023-11-23 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/151975 |
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Reference:
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[1] Andreu, F., Léon, S. Segura de, Boccardo, L., Orsina, L.: Existence results for $L^1$ data of some quasi-linear parabolic problems with a quadratic gradient term and source.Math. Models Methods Appl. Sci. 12 (2002), 1-16. Zbl 1032.35099, MR 1880893, 10.1142/S0218202502001520 |
Reference:
|
[2] Arcoya, D., Carmona, J., Leonori, T., Martínez-Aparicio, P. J., Orsina, L., Petitta, F.: Existence and nonexistence of solutions for singular quadratic quasilinear equations.J. Differ. Equations 246 (2009), 4006-4042. Zbl 1173.35051, MR 2514734, 10.1016/j.jde.2009.01.016 |
Reference:
|
[3] Boccardo, L., Orsina, L., Porzio, M. M.: Existence results for quasilinear elliptic and parabolic problems with quadratic gradient terms and sources.Adv. Calc. Var. 4 (2011), 397-419. Zbl 1232.35068, MR 2844511, 10.1515/acv.2011.006 |
Reference:
|
[4] Dall'Aglio, A., Orsina, L., Petitta, F.: Existence of solutions for degenerate parabolic equations with singular terms.Nonlinear Anal., Theory Methods Appl. 131 (2016), 273-288. Zbl 1332.35188, MR 3427981, 10.1016/j.na.2015.06.030 |
Reference:
|
[5] Ouardy, M. El, Hadfi, Y. El, Ifzarne, A.: Existence and regularity results for a singular parabolic equations with degenerate coercivity.Discrete Contin. Dyn. Syst., Ser. S 15 (2022), 117-141. Zbl 07539661, MR 4361686, 10.3934/dcdss.2021012 |
Reference:
|
[6] Leoni, F., Pellacci, B.: Local estimates and global existence for strongly nonlinear parabolic equations with locally integrable data.J. Evol. Equ. 6 (2006), 113-144. Zbl 1109.35052, MR 2215635, 10.1007/s00028-005-0234-7 |
Reference:
|
[7] Lions, J. L.: Quelques méthodes de résolution des problèmes aux limites non linéaires.Dunod, Paris (1969), French. Zbl 0189.40603, MR 0259693 |
Reference:
|
[8] Martínez-Aparicio, P. J., Petitta, F.: Parabolic equations with nonlinear singularities.Nonlinear Anal., Theory Methods Appl. 74 (2011), 114-131. Zbl 1203.35155, MR 2734981, 10.1016/j.na.2010.08.023 |
Reference:
|
[9] Rakotoson, J. M.: A compactness lemma for quasilinear problems: Application to parabolic equations.J. Funct. Anal. 106 (1992), 358-374. Zbl 0801.35063, MR 1165860, 10.1016/0022-1236(92)90053-L |
Reference:
|
[10] Simon, J.: Compact sets in the space $L^p(0,T;B)$.Ann. Mat. Pura Appl. (4) 146 (1987), 65-96. Zbl 0629.46031, MR 0916688, 10.1007/BF01762360 |
Reference:
|
[11] Souilah, R.: Existence and regularity results for some elliptic equations with degenerate coercivity and singular quadratic lower-order terms.Mediterr. J. Math. 16 (2019), Article ID 87, 21 pages. Zbl 1418.35177, MR 3969260, 10.1007/s00009-019-1360-8 |
Reference:
|
[12] Xia, L., Liu, Q., Yao, Z.: Existence of the maximal weak solution for a class of singular parabolic equations.J. Math. Anal. Appl. 387 (2012), 439-446. Zbl 1231.35105, MR 2845763, 10.1016/j.jmaa.2011.09.011 |
Reference:
|
[13] Xia, L., Yao, Z.: Existence, uniqueness and asymptotic behavior of solutions for a singular parabolic equation.J. Math. Anal. Appl. 358 (2009), 182-188. Zbl 1172.35421, MR 2527591, 10.1016/j.jmaa.2009.04.039 |
Reference:
|
[14] Zhang, C., Zhou, S.: Renormalized and entropy solutions for nonlinear parabolic equations with variable exponents and $L^1$ data.J. Differ. Equations 248 (2010), 1376-1400. Zbl 1195.35097, MR 2593046, 10.1016/j.jde.2009.11.024 |
Reference:
|
[15] Zhou, W., Wei, X.: Some results on a singular parabolic equation in one dimension case.Math. Methods Appl. Sci. 36 (2013), 2576-2587. Zbl 1280.35071, MR 3144123, 10.1002/mma.2778 |
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