On porous-elastic system with a time-varying delay term in the internal feedbacks

被引：6

作者：

Borges Filho, E. ^{[1
]}

Santos, M. L. ^{[1
]}

机构：

[1] Fed Univ Para, Inst Exact & Nat Sci, Doctoral Program Math, BR-66075110 Belem, Para, Brazil

来源：

ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK | 2020年 / 100卷 / 08期

关键词：

exponential decay; global solutions; time-varying delay; THERMOELASTIC SYSTEM; GENERAL DECAY; EXPONENTIAL DECAY; WAVE-EQUATION; 2ND SOUND; STABILITY; BOUNDARY; MEMORY;

D O I：

10.1002/zamm.201800247

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we consider the one-dimensional equations of an homogeneous and isotropic porous-elastic solid with interior time-dependent delay term feedbacks. First, using the variable norm technique of T. Kato, we prove that the system is well-posed under some hypothesis adopted. Then, via a suitable Lyapunov functional, we show that the system is exponentially stable.

引用

页数：22

共 29 条

[11] Conditions for robustness and nonrobustness of the stability of feedback systems with respect to small delays in the feedback loop
Logemann, H
Rebarber, R
Weiss, G
[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1996, 34 (02) : 572 - 600
[12] On the time decay of solutions in one-dimensional theories of porous materials
Magaña, A
Quintanilla, R
[J]. INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, 2006, 43 (11-12) : 3414 - 3427
[13] MESSAOUDI SA, 2014, ARAB J MATH SCI, V20, P213
[14] EXPONENTIAL DECAY FOR LINEAR DAMPED POROUS THERMOELASTIC SYSTEMS WITH SECOND SOUND
Messaoudi, Salim A.
Fareh, Abdelfeteh
[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2015, 20 (02): : 599 - 612
[15] GENERAL DECAY FOR A POROUS-THERMOELASTIC SYSTEM WITH MEMORY: THE CASE OF NONEQUAL SPEEDS
Messaoudi, Salim A.
Fareh, Abdelfeteh
[J]. ACTA MATHEMATICA SCIENTIA, 2013, 33 (01) : 23 - 40
[16] General decay for a porous thermoelastic system with memory: The case of equal speeds
Messaoudi, Salim A.
Fareh, Abdelfeteh
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (18) : 6895 - 6906
[17] On the time polynomial decay in elastic solids with voids
Munoz-Rivera, Jaime
Quintanilla, Ramon
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 338 (02) : 1296 - 1309
[18] Stability and instability results of the wave equation with a delay term in the boundary or internal feedbacks
Nicaise, Serge
Pignotti, Cristina
[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2006, 45 (05) : 1561 - 1585
[19] EXPONENTIAL STABILITY OF THE WAVE EQUATION WITH BOUNDARY TIME-VARYING DELAY
Nicaise, Serge
Pignotti, Cristina
Valein, Julie
[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2011, 4 (03): : 693 - 722
[20] NUNZIATO JW, 1979, ARCH RATION MECH AN, V72, P175, DOI 10.1007/BF00249363

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