Using Leray-Schauder topological degree to solve a linear diffusion parabolic equation with periodic initial conditions

Document Type : Research Paper

Authors

1 Department of Mathematics, College of Education for Pure Sciences, Tikrit University, Tikrit, Iraq

2 Department of Mathematics, College of Basic Education, Mustansiriyah University, Baghdad, Iraq

3 Department of Mathematics, College of Education, Al- Hamdaniya University, Mosul, Iraq

4 Department of Mathematics, College of Sciences, Kirkuk University, Kirkuk, Iraq

10.22075/ijnaa.2022.5777

Abstract

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.

Keywords