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The existence of periodic solutions to doubly degenerate Allen-Cahn equation with Neumann boundary condition | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 30، دوره 13، شماره 1، خرداد 2022، صفحه 397-408 اصل مقاله (407.2 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.5505 | ||
| نویسندگان | ||
| Raad Awad Hameed* 1؛ Maan A. Rasheed2؛ Hekmat Sh. Mustafa3؛ Faez N. Ghaffoori2 | ||
| 1Department of Mathematics, College of education for pure science, Tikrit University, Iraq | ||
| 2Department of Mathematics, College of Basic Education, Mustansiriyah University, Baghdad, Iraq | ||
| 3Department of Mathematics, College of Education, Al- Hamdaniya University, Mosul, Iraq | ||
| تاریخ دریافت: 19 مرداد 1400، تاریخ بازنگری: 12 شهریور 1400، تاریخ پذیرش: 04 مهر 1400 | ||
| چکیده | ||
| This work is concerned with the periodic solution of a doubly degenerate Allen-Cahn equation with nonlocal terms associated with Neumann boundary conditions. Firstly, we define a new associated auxiliary problem. Secondly, the topological degree theorem is applied to prove the existence of a limit point to the auxiliary problem, where this limit point represents a nontrivial nonnegative time-periodic solution of the main studied problem. It is observed that the topological degree theorem technique plays an important role in proving the desired results. Furthermore, this technique can be applied to other similar equations with homogeneous Dirichlet or Neumann boundary conditions. | ||
| کلیدواژهها | ||
| Degenerate Allen-Cahn equation؛ Neumann boundary conditions؛ Time-periodic solution؛ Topological degree theorem | ||
| مراجع | ||
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