Entropy solution for a nonlinear degenerate parabolic problem in weighted Sobolev space via Rothe's time-discretization approach
Resumo
In this paper, we prove the existence and uniqueness results of an entropy solution to a class of nonlinear degenerate parabolic problem with Dirichlet-type boundary condition and L1 data. The main tool used here is the Rothe's time-discretization approach combined with the theory of weighted Sobolev spaces.
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Referências
A. Abassi, A. El Hachimi, A. Jamea, Entropy solutions to nonlinear Neumann problems with L1-data, International Journal of Mathematics and Statistics 2(2008), 4–17.
Ph. Benilan, L. Boccardo, T. Gallouet, R. Gariepy, M. Pierre, J.L. Vazquez, An L1 theory of existence and uniqueness of solutions of nonlinear elliptic equations, Ann. Sc. Norm. Super. Pisa Cl. Sci. 22(1995), 241–273.
L. Boccardo, T. Gallouet, Nonlinear elliptic equations with right hand side measures, Comm. P.D.E. 17 (1992), 641-655. DOI: https://doi.org/10.1080/03605309208820857
L. Boccardo, T. Gallouet, Strongly nonlinear elliptic equations having natural growth terms and L1 data, Non Linear Analysis TMA, vol. 19, no 6, pp. 573-579, 1992. DOI: https://doi.org/10.1016/0362-546X(92)90022-7
A. C. Cavalheiro, Weighted Sobolev spaces and degenerate elliptic equations, Bol. Soc. Paran. Mat. 26(2008), 117-132. DOI: https://doi.org/10.5269/bspm.v26i1-2.7415
A. C. Cavalheiro, Existence and uniqueness of solutions for some degenerate nonlinear Dirichlet problems. J. Appl. Anal. 19, 41-54 (2013). DOI: https://doi.org/10.1515/jaa-2013-0003
Y. Chen, S. Levine, M. Rao, Variable exponent, linear growth functionals in image restoration, SIAM J. Appl. Math. 66(2006), 1383–1406. DOI: https://doi.org/10.1137/050624522
P. Drabek, A. Kufner, V. Mustonen, Pseudo-monotonicity and degenerated or singular elliptic operators, Bull. Austral. Math. Soc. 58(1998), 213-221. DOI: https://doi.org/10.1017/S0004972700032184
A. El Hachimi, A. Jamea, Nonlinear parabolic problems with Neumann-type boundary conditions and L1-data, Electron. J. Qual. Theory Differ. Equ., 27, 1–22 (2007). DOI: https://doi.org/10.14232/ejqtde.2007.1.27
G. Gagneux, M. Madaune-Tort, Analyse mathematique de modeles non lineaires de l’ingenierie petroliere, Mathematiques et apptications, vol. 22 Springer, 1996.
P. A. Hasto, The p(x)-Laplacian and applications, Proceedings of the International Conference on Geometric Function Theory 15(2007), 53–62
M. Ruzicka, Electrorheological Fluids, Modeling and Mathematical Theory, Lectures Notes in Math.,Vol. 1748, Springer, Berlin, 2000. DOI: https://doi.org/10.1007/BFb0104030
A. Sabri, A. Jamea, H. A. Talibi, Existence of entropy solutions to nonlinear degenerate parabolic problems with variable exponent and L1-data, Communications in Mathematics, 28 (2020) 67-88. DOI: https://doi.org/10.2478/cm-2020-0006
A. Sabri, A. Jamea, Rothe time-discretization method for a nonlinear parabolic p(u) -Laplacian problem with Fouriertype boundary condition and L1-data. Ricerche mat (2020). DOI: https://doi.org/10.1007/s11587-020-00544-2
A. Sabri, A. Jamea, H. A. Talibi, Weak solution for nonlinear degenerate elliptic problem with Dirichlet-type boundary condition in weighted Sobolev spaces, Mathematica Bohemica, Vol. 147, No. 1, pp. 113-129, 2022
A. Sabri, A. Jamea and H. A. Talibi, Entropy solution for a nonlinear degenerate elliptic problem with Dirichlettype boundary condition in weighted Sobolev spaces, Le Matematiche, Vol. LXXVI (2021)-Issue I, pp. 109-131. DOI: https://doi.org/10.21136/MB.2021.0004-20
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