Title of article
The existence of periodic solutions to doubly degenerate Allen-Cahn equation with Neumann boundary condition
Author/Authors
Hameed, Raad Awad Department of Mathematics - College of education for pure science - Tikrit University, Iraq , Rasheed, Maan A. Department of Mathematics - College of Basic Education - Mustansiriyah University, Baghdad, Iraq , Mustafa, Hekmat Sh. Department of Mathematics - College of Education - Al- Hamdaniya University, Mosul, Iraq , Ghaffoori, Faez N. Department of Mathematics - College of Basic Education - Mustansiriyah University, Baghdad, Iraq
Pages
12
From page
397
To page
408
Abstract
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.
Keywords
Degenerate Allen-Cahn equation , Neumann boundary conditions , Time-periodic solution , Topological degree theorem
Journal title
International Journal of Nonlinear Analysis and Applications
Serial Year
2022
Record number
2711241
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