Global existence and decay estimates for the semilinear heat equation with memory in $\mathbb{R}^{n}$

	Global existence and decay estimates for the semilinear heat equation with memory in $\mathbb{R}^{n}$
International Journal of Nonlinear Analysis and Applications
مقاله 183، دوره 13، شماره 2، مهر 2022، صفحه 2271-2285 اصل مقاله (465.2 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.22713.2407
نویسندگان
Mohamed Berbiche^* ¹؛ Ammar Melik²
¹Laboratory of Mathematical Analysis, Probability and Optimizations, University of Biskra, Po. Box 145 Biskra (07000), Algeria
²Department of Mathematics, Mohamed Khider University, B.P. 145, 07000, Biskra, Algeria
چکیده
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.
کلیدواژه‌ها
Integro-partial differential equations؛ Global existence؛ Decay estimates
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