Non-solvability of Balakrishnan-Taylor system with memory term in \(\mathbb{R}^{N}\)
Volume 22, Issue 2, pp 110--118
http://dx.doi.org/10.22436/jmcs.022.02.02
Publication Date: July 15, 2020
Submission Date: April 22, 2019
Revision Date: February 06, 2020
Accteptance Date: February 12, 2020
-
1079
Downloads
-
2366
Views
Authors
Mourad Benzahi
- Department of Mathematics and Computer Science, LAMIS Laboratory, Larbi Tebessi University, 12002 Tebessa, Algeria.
Abdelrahmane Zarai
- Department of Mathematics and Computer Science, LAMIS Laboratory, Larbi Tebessi University, 12002 Tebessa, Algeria.
Salem Abdelmalek
- Department of Mathematics and Computer Science, LAMIS Laboratory, Larbi Tebessi University, 12002 Tebessa, Algeria.
Samir Bendoukha
- Electrical Engineering Department, College of Engineering at Yanbu, Taibah University, Saudi Arabia.
Abstract
This study establishes a novel nonexistence result for a strongly coupled viscoelastic system with Balakrishnan-Taylor damping and a nonlinear source in the whole space. Sufficient conditions ensuring the nonexistence of solutions are established using the test function method.
Share and Cite
ISRP Style
Mourad Benzahi, Abdelrahmane Zarai, Salem Abdelmalek, Samir Bendoukha, Non-solvability of Balakrishnan-Taylor system with memory term in \(\mathbb{R}^{N}\), Journal of Mathematics and Computer Science, 22 (2021), no. 2, 110--118
AMA Style
Benzahi Mourad, Zarai Abdelrahmane, Abdelmalek Salem, Bendoukha Samir, Non-solvability of Balakrishnan-Taylor system with memory term in \(\mathbb{R}^{N}\). J Math Comput SCI-JM. (2021); 22(2):110--118
Chicago/Turabian Style
Benzahi, Mourad, Zarai, Abdelrahmane, Abdelmalek, Salem, Bendoukha, Samir. "Non-solvability of Balakrishnan-Taylor system with memory term in \(\mathbb{R}^{N}\)." Journal of Mathematics and Computer Science, 22, no. 2 (2021): 110--118
Keywords
- Balakrishnan-Taylor system
- non-solvability
- memory term
MSC
References
-
[1]
A. V. Balakrishnan, L. W. Taylor, Distributed parameter nonlinear damping models for flight structures, Proceedings , WPAFB (1989)
-
[2]
R. W. Bass, D. Zes, Spillover, nonlinearity, and flexible structures, 4th NASA Workshop on Computational Control of Flexible Aerospace Systems, 1991 (1991), 1--14
-
[3]
H. R. Clark, Elastic membrane equation in a bounded and unbounded domains, Electron. J. Qualit. Theor. Differ. Equ., 2002 (2002), 1--21
-
[4]
T. G. Ha, General decay rate estimates for viscoelastic wave equation with Balakrishnan--Taylor damping, Z. Angew. Math. Phys., 67 (2016), 13 pages
-
[5]
T. G. Ha, Stabilization for the wave equation with variable coefficients and Balakrishnan--Taylor damping, Taiwanese J. Math., 21 (2017), 807--817
-
[6]
E. Mitidieri, S. I. Pohozaev, Apriori estimates and blow--up of solutions to nonlinear partial differential equations and inequalities, Proc. Steklov Inst. Math., 234 (2001), 1--383
-
[7]
C. Mu, J. Ma, On a system of nonlinear wave equations with Balakrishnan--Taylor damping, Z. Angew. Math. Phys., 65 (2014), 91--113
-
[8]
S. H. Park, Arbitrary decay of energy for a viscoelastic problem with BalakrishnanTaylor damping, Taiwanese J. Math., 20 (2016), 129--141
-
[9]
N. E. Tatar, A. Zaraï, Exponential stability and blow up for a problem with Balakrishnan-Taylor damping, Demonstratio Math., 44 (2011), 67--90
-
[10]
N. E. Tatar, A. Zaraï, On a Kirchhoff equation with Balakrishnan--Taylor damping and source term, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., 18 (2011), 615--627
-
[11]
S. T. Wu, General decay of solutions for a viscoelastic equation with Balakrishnan--Taylor damping and nonlinear boundary damping--source interactions, Acta Math. Sci., 35 (2015), 981--994
-
[12]
Y. You, Inertial manifolds and stabilization of nonlinear beam equations with Balakrishnan--Taylor damping, Abst. Appl. Anal., 1 (1996), 83--102
-
[13]
A. Zaraï, N. E. Tatar, Global existence and polynomial decay for a problem with Balakrishnan-Taylor damping, Arch. Math. (Brno), 46 (2010), 157--176
-
[14]
A. Zaraï, N. E. Tatar, Non--solvability of Balakrishnan--Taylor equation with memory term in $\mathbb{R}^{N}$, Adv. Appl. Math. Approx. Theory, 41 (2013), 411--419
-
[15]
A. Zaraï, N. E. Tatar, S. Abdelmalek, Elastic membrance equation with memory term and nonlinear boundary damping: global existence, decay and blowup of the solution, Acta Math. Sci., 33 (2013), 84--106