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Using Leray-Schauder topological degree to solve a linear diffusion parabolic equation with periodic initial conditions | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 133، دوره 13، شماره 1، خرداد 2022، صفحه 1629-1635 اصل مقاله (367.79 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.5777 | ||
| نویسندگان | ||
| Raad Awad Hameed* 1؛ Faez N. Ghaffoori2؛ Hekmat sh. Mustafa3؛ Wafaa M. Taha4؛ Maan A. Rasheed2 | ||
| 1Department of Mathematics, College of Education for Pure Sciences, Tikrit University, Tikrit, Iraq | ||
| 2Department of Mathematics, College of Basic Education, Mustansiriyah University, Baghdad, Iraq | ||
| 3Department of Mathematics, College of Education, Al- Hamdaniya University, Mosul, Iraq | ||
| 4Department of Mathematics, College of Sciences, Kirkuk University, Kirkuk, Iraq | ||
| تاریخ دریافت: 25 شهریور 1400، تاریخ بازنگری: 18 مهر 1400، تاریخ پذیرش: 08 آذر 1400 | ||
| چکیده | ||
| Throughout this manuscript, we show time periodic solutions to a linear diffusion parabolic equation with Diriclet condition. Based on the topological degree theorem, we prove a time periodic solutions of the system such that we found the fixed point when the domain of the solution is sufficiently small. | ||
| کلیدواژهها | ||
| weakly nonlinear sources؛ Diriclet boundary conditions؛ Time-periodic solution؛ Topological degree theorem | ||
| مراجع | ||
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[1] N. Alaa and M. Iguernane, Weak periodic solutions of some quasilinear parabolic equations with data measures, J. Inequal. Pure Appl. Math. 3(3) (2002) Article 46. [2] R.A. Hameed, J. Sun and B. Wu, Existence of periodic solutions of a p-Laplacian-Neumann problem, Boundary Value Prob. 171 (2013) 1–11. [3] R.A. Hameed, B. Wu and J. Sun, Periodic solution of a quasilinear parabolic equation with nonlocal terms and Neumann boundary conditions”, Boundary Value Prob. 34(2013) 1–11. [4] R.A. Hameed, M.A. Rasheed, H.S. Mustafa and F.N. Ghaffoori, The existence of periodic solutions to doubly degenerate Allen-Cahn equation with Neumann boundary condition, Int. J. Nonlinear Anal. Appl. 13(1) (2022) 397–408. [5] L.G. Khoma and N.G. Khoma, Generalized periodic solutions of quasilinear equations, Ukr. Math. J. 48(3) (1996) 453–459. [6] G.M. Lieberman, Time-periodic solutions of quasilinear parabolic differential equations: I Dirichlet boundary conditions, J. Math. Anal. Appl. 264(2) (2001) 617–638. [7] Z.H. Liu, Periodic solutions for double degenerate quasilinear parabolic equations, Nonlinear Anal. 51(7) (2002) 1245–1257. [8] B.P. Liu and C.V. Pao, Periodic solutions of coupled semilinear parabolic boundary value problems, Nonlinear Anal. 6(3) (1982) 237–252. [9] O.A. Ladyzenskaja, V.A. Solonnikov and N.N. Ural’ceva, Linear and Quasilinear Equations of Parabolic Type, Translation of Mathematical Monographs, vol. 23. Amer. Math. Soc. Providence, 1968. [10] I.I. Smulev, Periodic solutions of the first boundary value problem for parabolic equations, Amer. Math. Soc. Transl. Set 79(2) (1969) 215–229. [11] D.G. Guo, Nonlinear Functional Analysis, Shandong Science and Technology Press, Jinan, 2001. | ||
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