On the solution of evolution p(.)-Bilaplace equation with variable

Resumo

A high-order parabolic p(.)-Bilaplace equation with variable exponent is studied. The well-posedness at each time step of the problem in suitable Lebesgue Sobolev spaces with variable exponent with the help of nonlinear monotone operators theory is investigated. The solvability of the proposed problem as well as some regulrarity results are shown using Roth-Galerkin method.

Downloads

Não há dados estatísticos.

Biografia do Autor

Prof. Abderrazek Chaoui, University 8 May 1945

Department of Mathematics

Manal Djaghout, University 8 May 1945

Department of Mathematics

Referências

Kovaik, O. and Rakosnik, J., On the spaces Lp(x) (Ω) and W1,p(x) (Ω), Czechoslovak Math.J., 41(4), 592-618, (1991). DOI: https://doi.org/10.21136/CMJ.1991.102493

Samko, S., Convolution type operators in Lp(x) (Rn), Integral transform. Spec. Funct., 7,123-144, (1998). DOI: https://doi.org/10.1080/10652469808819191

Fan, X. L., Wang, S. Y. and Zhao, D., Density of C∞(Ω) in W1,p(x) (Ω) with discontinous exponent p(x), Math. Nachr., 279(1-3), 142-149, (2006). DOI: https://doi.org/10.1002/mana.200310351

Fan, X. L. and Zhao, D., On the spaces Lp(x) (Ω) and W1,p(x) (Ω), J. Math. Anal. Appl., 263, 424-446, (2001). DOI: https://doi.org/10.1006/jmaa.2000.7617

Diening, L., Harjulehto, P.i., Hasto, P. and Ruzicka, M., Lebesgue and Sobolev spaces with variable exponents, SPIN Springer’s internal project number. December 3, (2010). DOI: https://doi.org/10.1007/978-3-642-18363-8

Georgoulis, E. H. and Houston, P., Discontinuous Galerkin methods for the biharmonic problem, IMA J. Numer. Anal., 293, 573-594, (2009). DOI: https://doi.org/10.1093/imanum/drn015

Pryer, T., Discontinuous Galerkin methods for the p-biharmonic equation from a discrete variational perspective, Electr. Transac. Nume. Anal., 41, 328-349, 2014.

Lindqvist, P.,Notes on the p-Laplace equation, NO-7491, Trondheim, Norway.

Becache, E., Ciarlet, P., Hazard, C., and Luneville, E., La methode des elements finis De la theorie a la pratique II. Complements, Les presse de l’ENSTA.

Li, H., The W1,p stability of the Ritz projection on graded meshes, Math. Comput., 86303, 49-74, (2017). DOI: https://doi.org/10.1090/mcom/3101

Sandri, D., Sur l’approximation numerique des ecoulements quasi-newtoniens dont la viscosite suit la loi puissance ou la loi de Carreau, RAIRO Model. Math. Anal. Number, 272, 131-155, (1993). DOI: https://doi.org/10.1051/m2an/1993270201311

Gyulov, T. and Moro sanu, G.,On a class of boundary value problems involving the pbiharmonic operator, J. Math. Anal. Appl. 367(1), 43-57, (2010). DOI: https://doi.org/10.1016/j.jmaa.2009.12.022

Lazer, A. and McKenna, P., Large-amplitude periodic oscillations in suspension bridges: some newconnections with nonlinear analysis, Siam Review, 32(4), 537-578, (1990). DOI: https://doi.org/10.1137/1032120

Theljani, A., Belhachmi, Z. and Moakher, M., High-order anisotropic diffusion operators in spaces of variable exponents and application to image inpainting and restoration problems, Nonl. Anal.: Real World Appl., 47, 251-271, (2019). DOI: https://doi.org/10.1016/j.nonrwa.2018.10.013

Chaoui, A. and Hallaci, A., On the solution of a fractional diffusion integrodifferential equation with Rothe time discretization, Numerical Functional Analysis and Optimization, DOI : 10.1080/01630563.2018.1424200.

Chaoui, A. and Guezane-Lakoud, A., Solution to an integrodifferential equation with integral condition, Applied Mathematics and Computation, 266(2015) 903-908. DOI: https://doi.org/10.1016/j.amc.2015.06.004

Chaoui, A. and Rezgui, N., Solution to fractional pseudoparabolic equation with fractional integral condition, Red. Circ. Mat. Palermo, II. Ser., DOI 10.1007/s12215-017-0306-x.

Crouzeix, M. and Thomee, V., The stability in Lp and W1 p of the L2-projection onto finite element function spaces, Math. Comp. 48 (1987), no. 178, 521–532. MR878688(88f:41016). DOI: https://doi.org/10.2307/2007825

Publicado
2022-12-28
Seção
Artigos