Tytuł artykułu
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Języki publikacji
Abstrakty
This paper is devoted to study the global existence of solutions of the hyperbolic Dirichlet equation Utt=Lu+f(x,t) in ΩT=Ω×(0,T), where L is a nonlinear operator and ϕ(x,t,⋅), f(x,t) and the exponents of the nonlinearities p(x,t) and μ(x,t) are given functions.
Wydawca
Czasopismo
Rocznik
Tom
Strony
55--69
Opis fizyczny
Bibliogr. 35 poz.
Twórcy
autor
- Laboratory LAMA, Department of Mathematics, Faculty of Sciences Dhar El Mahraz, University of Fez, B.P 1796 Atlas Fez, Morocco
autor
- Laboratory LAMA, Department of Mathematics, Faculty of Sciences Dhar El Mahraz, University of Fez, B.P 1796 Atlas Fez, Morocco
autor
- Laboratory LISA, Department of Electrical and Computer Engineering, National School of Applied Sciences, University of Fez, Fez, Morocco
autor
- Laboratory LSI, Department of Mathematics and Physics and Informatics, Polydisciplinary Faculty of Taza, University of Fez, Taza, Morocco
Bibliografia
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- [3] S. Antontsev, J. I. Diaz and S. Shmarev, Energy Methods for Free Boundary Problems: Applications to Non-Linear PDEs and Fluid Mechanics, Progr. Nonlinear Differential Equations Appl. 48, Birkhäuser, Boston, 2002.
- [4] S. Antontsev and J. F. Rodrigues, On stationary thermo-rheological viscous flows, Ann. Univ. Ferrara Sez. VII Sci. Mat. 52 (2006), 19-36.
- [5] S. Antontsev and S. I. Shmarev, Elliptic equations with anisotropic nonlinearity and nonstandard growth conditions, in: Handbook of Differential Equations, Stationary Partial Differential Equations. Vol. 3, Elsevier, Amsterdam (2006), 1-100.
- [6] S. Antontsev and S. I. Shmarev, Localization of solutions of anisotropic parabolic equations, Nonlinear Anal. 71 (2009), e725-e737.
- [7] S. Antontsev and S. I. Shmarev, Parabolic equations with anisotropic nonstandard growth conditions, in: Free Boundary Problems. Theory and Applications, Internat. Ser. Numer. Math. 154, Birkhäuser, Basel (2006), 33-44.
- [8] S. Antontsev and V. Zhikov, Higher integrability for parabolic equations of p(x, t)-Laplacian type, Adv. Differential Equations 10 (2005), 1053-1080.
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- [16] M. Dreher, The wave equation for the p-Laplacian, Hokkaido Math. J. 36 (2007), 21-52.
- [17] X. L. Fan and D. Zhao, On the generalised Orlicz-Sobolev Space Wk,p(x)(Ω), J. Gansu Educ. College 12 (1998), no. 1, 1-6.
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- [26] G. Todorova and E. Vitillario, Blow-up for nonlinear dissipative wave equations in ℝn, J. Math. Anal. Appl. 303 (2005), 242-257.
- [27] Z. Wilstein, Global well-posedness for a nonlinear wave equation with p-Laplacian damping, Dissertation, University of Nebraska-Lincoln, 2011, http://digitalcommons.unl.edu/mathstudent/24.
- [28] Z. Yang, Cauchy problem for quasi-linear wave equations with viscous damping, J. Math. Anal. Appl. 320 (2006), 859-881.
- [29] Z. Yang and G. Chen, Global existence of solutions for quasi-linear wave equations with viscous damping, J. Math. Anal. Appl. 285 (2003), 604-618.
- [30] D. Zhao, W. J. Qiang and X. L. Fan, On generalized Orlicz spaces Lp(x)(Ω), J. Gansu Sci. 9 (1997), no. 2.
- [31] Y. Zhijian, Existence and asymptotic behaviour of solutions for a class of quasi-linear evolution equations with non-linear damping and source terms, Math. Methods Appl. Sci. 25 (2002), 795-814.
- [32] Y. Zhijian, Global existence, asymptotic behavior and blowup of solutions for a class of nonlinear wave equations with dissipative term, J. Differential Equations 187 (2003), 520-540.
- [33] Y. Zhijian, Initial boundary value problem for a class of non-linear strongly damped wave equations, Math. Methods Appl. Sci. 26 (2003), 1047-1066.
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Uwagi
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-6abcd4bf-0828-48e6-8605-3d8abdcf9762