Geodesic
Existence results for some nonlinear parabolic equations with degenerate coercivity and singular lower-order terms
Mathematica Bohemica, Tome 148 (2023) no. 4, pp. 561-581
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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 $L^1$.
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 $L^1$.
DOI : 10.21136/MB.2022.0152-21
Classification : 35K55, 35K65, 35K67
Keywords: singular equation; nonlinear parabolic equation; degenerate coercivity 
@article{10_21136_MB_2022_0152_21,
     author = {Mecheter, Rabah and Mokhtari, Fares},
     title = {Existence results for some nonlinear parabolic equations with degenerate coercivity and singular lower-order terms},
     journal = {Mathematica Bohemica},
     pages = {561--581},
     year = {2023},
     volume = {148},
     number = {4},
     doi = {10.21136/MB.2022.0152-21},
     mrnumber = {4673838},
     zbl = {07790604},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2022.0152-21/}
}
TY  - JOUR
AU  - Mecheter, Rabah
AU  - Mokhtari, Fares
TI  - Existence results for some nonlinear parabolic equations with degenerate coercivity and singular lower-order terms
JO  - Mathematica Bohemica
PY  - 2023
SP  - 561
EP  - 581
VL  - 148
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2022.0152-21/
DO  - 10.21136/MB.2022.0152-21
LA  - en
ID  - 10_21136_MB_2022_0152_21
ER  - 
%0 Journal Article
%A Mecheter, Rabah
%A Mokhtari, Fares
%T Existence results for some nonlinear parabolic equations with degenerate coercivity and singular lower-order terms
%J Mathematica Bohemica
%D 2023
%P 561-581
%V 148
%N 4
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2022.0152-21/
%R 10.21136/MB.2022.0152-21
%G en
%F 10_21136_MB_2022_0152_21
Mecheter, Rabah; Mokhtari, Fares. Existence results for some nonlinear parabolic equations with degenerate coercivity and singular lower-order terms. Mathematica Bohemica, Tome 148 (2023) no. 4, pp. 561-581. doi: 10.21136/MB.2022.0152-21

[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. | DOI | MR | JFM

[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. | DOI | MR | JFM

[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. | DOI | MR | JFM

[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. | DOI | MR | JFM

[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. | DOI | MR | JFM

[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. | DOI | MR | JFM

[7] Lions, J. L.: Quelques méthodes de résolution des problèmes aux limites non linéaires. Dunod, Paris (1969), French. | MR | JFM

[8] Martínez-Aparicio, P. J., Petitta, F.: Parabolic equations with nonlinear singularities. Nonlinear Anal., Theory Methods Appl. 74 (2011), 114-131. | DOI | MR | JFM

[9] Rakotoson, J. M.: A compactness lemma for quasilinear problems: Application to parabolic equations. J. Funct. Anal. 106 (1992), 358-374. | DOI | MR | JFM

[10] Simon, J.: Compact sets in the space $L^p(0,T;B)$. Ann. Mat. Pura Appl. (4) 146 (1987), 65-96. | DOI | MR | JFM

[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. | DOI | MR | JFM

[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. | DOI | MR | JFM

[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. | DOI | MR | JFM

[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. | DOI | MR | JFM

[15] Zhou, W., Wei, X.: Some results on a singular parabolic equation in one dimension case. Math. Methods Appl. Sci. 36 (2013), 2576-2587. | DOI | MR | JFM

Cité par Sources :