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Entropy solution for doubly nonlinear elliptic anisotropic problems with Fourier boundary conditions

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EN
Abstrakty
EN
The goal of this paper is to study nonlinear anisotropic problems with Fourier boundary conditions. We first prove, by using the technic of monotone operators in Banach spaces, the existence of weak solutions, and by approximation methods, we prove a result of existence and uniqueness of entropy solution.
Twórcy
  • Laboratoire de Mathématiques et Informatique (LAMI), UFR. Sciences et Techniques, Université Polytechnique de Bobo-Dioulasso, 01 BP 1091 Bobo 01, Bobo-Dioulasso, Burkina Faso
  • Laboratoire de Mathématiques et Informatique (LAMI), UFR. Sciences Exactes et Appliquées, Université de Ouagadougou, 03 BP 7021 Ouaga 03, Ouagadougou, Burkina Faso
Bibliografia
  • [1] S.N. Antontsev and J.F. Rodrigues, On stationary thermorheological viscous flows, Annal. del Univ. de Ferrara 52 (2006), 19-36. doi: 10.1007/s11565-006-0002-9
  • [2] B.K. Bonzi and S. Ouaro, Entropy solution for a doubly nonlinear elliptic problem with variable exponent, J. Math. Anal. Appl. 370 (2) (2010), 392-405. doi: 10.1016/j.jmaa.2010.05.022
  • [3] B.K. Bonzi, S. Ouaro and F.D.Y. Zongo, Nonlinear elliptic anisotropic problem with Fourier boundary condition, Int. J. Evol. Equ. 8 (4) (2013), 305-328.
  • [4] B.K. Bonzi, S. Ouaro and F.D.Y. Zongo, Entropy solutions to nonlinear elliptic anisotropic problem with Robin boundary condition, Matematiche 68 (2013), 53-76.
  • [5] B.K. Bonzi, S. Ouaro and F.D.Y. Zongo, Entropy solutions for nonlinear elliptic anisotropic homogeneous Neumann problem, Int. J. Differ. Equ. Article 476781 (2013), pp. 14. doi: 10.1155/2013/476781
  • [6] M. Boureanu and V. D. Radulescu, Anisotropic Neumann problems in Sobolev spaces with variable exponent, Nonlin. Anal. 75 (2012), 4471-4482. doi: 10.1016/j.na.2011.09.033
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  • [8] X. Fan, Anisotropic variable exponent Sobolev spaces and $\vec{p}(·)$-Laplacian equations, Complex Var. Elliptic Equ. 55 (2010), 1-20. doi: 10.1080/17476930902999082
  • [9] X. Fan and D. Zhao, On the spaces $L^{p(x)}(Ω)$ and $W^{1,p(x)}(Ω)$, J. Math. Appl. 263 (2001), 424-446.
  • [10] B. Koné, S. Ouaro and S. Traoré, Weak solutions for anisotropic nonlinear elliptic equations with variable exponents, Electron. J. Diff. Equ. 144 (2009), 1-11.
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  • [12] M. Mihailescu, P. Pucci and V. Radulescu, Eigenvalue problems for anisotropic quasilinear elliptic equations with variable exponent, J. Math. Anal. Appl. 340 (2008), 687-698. doi: 10.1016/j.jmaa.2007.09.015
  • [13] M. Mihailescu and V. Radulescu, A multiplicity result for a nonlinear degenerate problem arising in the theory of electrorheological fluids, Proc. R. Soc. A 462 (2006), 2625-2641. doi: 10.1098/rspa.2005.1633
  • [14] I. Nyanquini and S. Ouaro, Entropy solution for nonlinear elliptic problem involving variable exponent and Fourier type boundary condition, Afr. Mat. 23 (2012), 205-228. doi: 10.1007/s13370-011-0030-1
  • [15] S. Ouaro, Well-posedness results for anisotropic nonlinear elliptic equations with variable exponent and L¹-data, Cubo J. 12 (2010), 133-148. doi: 10.4067/S0719-06462010000100012
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  • [17] M. Troisi, Theoremi di inclusione per spazi di Sobolev non isotropi, Recherche. Mat. 18 (1969), 3-24.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1175
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