Global existence and decay estimates for the semilinear heat equation with memory in $\mathbb{R}^{n}$
نویسندگان
1 Laboratory of Mathematical Analysis, Probability and Optimizations, University of Biskra, Po. Box 145 Biskra (07000), Algeria
2 Department of Mathematics, Mohamed Khider University, B.P. 145, 07000, Biskra, Algeria
doi
10.22075/ijnaa.2021.22713.2407چکیده
In this paper, we study the initial value problem for a semi-linear heat equation with memory in $n$-dimensional space $\mathbb{R}^{n}$. Under a smallness conditions on the initial data, the global existence and decay estimates of the solutions are established. Furthermore, time decay estimates in higher Sobolev space of the solution are provided. The proof is carried out by means of the point-wise decay estimates of the solution in the Fourier space and a fixed point-contraction mapping argument.
