Global existence and decay estimates for the semilinear nonclassical-diffusion equations with memory in Rn

被引：0

作者：

Berbiche, Mohamed ^{[1
]}

Melik, Ammar ^{[1
]}

机构：

[1] Mohamed Khider Biskra Univ, Lab Math Anal Probabil & Optimizat, POB 145, Biskra 07000, Algeria

来源：

ADVANCED STUDIES-EURO-TBILISI MATHEMATICAL JOURNAL | 2022年 / 15卷 / 02期

关键词：

heat equation with memory; stabilization; global existence; decay estimates; HEAT-CONDUCTION; ATTRACTORS; STABILITY;

D O I：

10.32513/asetmj/19322008215

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study the initial value problem for a semi-linear nonclassical diffusion equations with fading memory in R-n. Under 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 pointwise decay estimates of the solution in the Fourier space and a fixed point-contraction mapping argument.

引用

页码：29 / 53

页数：25

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