TY - JOUR
ID - 5505
TI - The existence of periodic solutions to doubly degenerate Allen-Cahn equation with Neumann boundary condition
JO - International Journal of Nonlinear Analysis and Applications
JA - IJNAA
LA - en
SN - 2008-6822
AU - Hameed, Raad Awad
AU - Rasheed, Maan A.
AU - Mustafa, Hekmat Sh.
AU - Ghaffoori, Faez N.
AD - Department of Mathematics, College of education for pure science, Tikrit University, Iraq
AD - Department of Mathematics, College of Basic Education, Mustansiriyah University, Baghdad, Iraq
AD - Department of Mathematics, College of Education, Al- Hamdaniya University, Mosul, Iraq
Y1 - 2022
PY - 2022
VL - 13
IS - 1
SP - 397
EP - 408
KW - Degenerate Allen-Cahn equation
KW - Neumann boundary conditions
KW - Time-periodic solution
KW - Topological degree theorem
DO - 10.22075/ijnaa.2022.5505
N2 - 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.
UR - https://ijnaa.semnan.ac.ir/article_5505.html
L1 - https://ijnaa.semnan.ac.ir/article_5505_38a74da87b97ddb34ded83786807d966.pdf
ER -