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

共 25 条

[1] ON THE PROBLEM OF DIFFUSION IN SOLIDS [J].

AIFANTIS, EC .

ACTA MECHANICA, 1980, 37 (3-4) :265-296

[2]

Barenblatt GI., 1960, J. Appl. Math. Mech, V24, P1286, DOI [10.1016/0021-8928(60)90107-6, DOI 10.1016/0021-8928(60)90107-6]

[3]

Carroll RW, 1976, Singular and degenerate Cauchy problems

[4] ON A THEORY OF HEAT CONDUCTION INVOLVING 2 TEMPERATURES [J].

CHEN, PJ .

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 1968, 19 (04) :614-&

[5]

Chepyzhov VV, 2006, ASYMPTOTIC ANAL, V50, P269

[6] On trajectory and global attractors for semilinear heat equations with fading memory [J].

Chepyzhov, VV ;

Miranville, A .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2006, 55 (01) :119-167

[7] EQUIPRESENCE AND CONSTITUTIVE EQUATIONS FOR RIGID HEAT CONDUCTORS [J].

COLEMAN, BD ;

GURTIN, ME .

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 1967, 18 (02) :199-&

[8] Decay rates of Volterra equations on RN [J].

Conti, Monica ;

Gatti, Stefania ;

Pata, Vittorino .

CENTRAL EUROPEAN JOURNAL OF MATHEMATICS, 2007, 5 (04) :720-732

[9] A Remark on Nonclassical Diffusion Equations with Memory [J].

Conti, Monica ;

Marchini, Elsa M. .

APPLIED MATHEMATICS AND OPTIMIZATION, 2016, 73 (01) :1-21

[10] Nonclassical diffusion with memory [J].

Conti, Monica ;

Marchini, Elsa M. ;

Pata, Vittorino .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2015, 38 (05) :948-958

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