Exponential growth of positive initial energy for a system of higher-order viscoelastic wave equations with variable exponents
Abstract This work addresses a value problem concerning a system of high-order nonlinear equations with viscoelastic terms acting in both equations and homogeneous Dirichlet conditions. Initially, we demonstrate that the system has a weak local solution by combining fixed point theory and Galerkin’s...
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| Language: | English |
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2025-01-01
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| Series: | Journal of Inequalities and Applications |
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| Online Access: | https://doi.org/10.1186/s13660-024-03250-x |
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| author | Amar Ouaoua Wissem Boughamsa Salah Boulaaras |
| author_facet | Amar Ouaoua Wissem Boughamsa Salah Boulaaras |
| author_sort | Amar Ouaoua |
| collection | DOAJ |
| description | Abstract This work addresses a value problem concerning a system of high-order nonlinear equations with viscoelastic terms acting in both equations and homogeneous Dirichlet conditions. Initially, we demonstrate that the system has a weak local solution by combining fixed point theory and Galerkin’s method. Under certain conditions on the variable exponents p ( . ) $p(.)$ , as well as conditions related to the kernel functions η ( t ) ≤ μ ( t ) $\eta \left ( t\right ) \leq \mu \left ( t\right ) $ , for all t ≥ 0 $t\geq 0$ , we establish that the solution with positive initial energy exhibits exponential growth. In addition, we study some numerical examples to illustrate our theoretical results and demonstrate the effectiveness of our new approach. |
| format | Article |
| id | doaj-art-3a395aef8b7346c0a5e8b330c844e783 |
| institution | OA Journals |
| issn | 1029-242X |
| language | English |
| publishDate | 2025-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj-art-3a395aef8b7346c0a5e8b330c844e7832025-08-20T02:35:36ZengSpringerOpenJournal of Inequalities and Applications1029-242X2025-01-012025112710.1186/s13660-024-03250-xExponential growth of positive initial energy for a system of higher-order viscoelastic wave equations with variable exponentsAmar Ouaoua0Wissem Boughamsa1Salah Boulaaras2LAMAHIS Laboratory, University of 20 August 1955Department of Mathematics, LAMAHIS Laboratory, University of 20 August 1955Department of Mathematics, College of Science, Qassim UniversityAbstract This work addresses a value problem concerning a system of high-order nonlinear equations with viscoelastic terms acting in both equations and homogeneous Dirichlet conditions. Initially, we demonstrate that the system has a weak local solution by combining fixed point theory and Galerkin’s method. Under certain conditions on the variable exponents p ( . ) $p(.)$ , as well as conditions related to the kernel functions η ( t ) ≤ μ ( t ) $\eta \left ( t\right ) \leq \mu \left ( t\right ) $ , for all t ≥ 0 $t\geq 0$ , we establish that the solution with positive initial energy exhibits exponential growth. In addition, we study some numerical examples to illustrate our theoretical results and demonstrate the effectiveness of our new approach.https://doi.org/10.1186/s13660-024-03250-xHigher-order equationSource termViscoelastic termVariable-exponentExponential growthNonlinear equations |
| spellingShingle | Amar Ouaoua Wissem Boughamsa Salah Boulaaras Exponential growth of positive initial energy for a system of higher-order viscoelastic wave equations with variable exponents Journal of Inequalities and Applications Higher-order equation Source term Viscoelastic term Variable-exponent Exponential growth Nonlinear equations |
| title | Exponential growth of positive initial energy for a system of higher-order viscoelastic wave equations with variable exponents |
| title_full | Exponential growth of positive initial energy for a system of higher-order viscoelastic wave equations with variable exponents |
| title_fullStr | Exponential growth of positive initial energy for a system of higher-order viscoelastic wave equations with variable exponents |
| title_full_unstemmed | Exponential growth of positive initial energy for a system of higher-order viscoelastic wave equations with variable exponents |
| title_short | Exponential growth of positive initial energy for a system of higher-order viscoelastic wave equations with variable exponents |
| title_sort | exponential growth of positive initial energy for a system of higher order viscoelastic wave equations with variable exponents |
| topic | Higher-order equation Source term Viscoelastic term Variable-exponent Exponential growth Nonlinear equations |
| url | https://doi.org/10.1186/s13660-024-03250-x |
| work_keys_str_mv | AT amarouaoua exponentialgrowthofpositiveinitialenergyforasystemofhigherorderviscoelasticwaveequationswithvariableexponents AT wissemboughamsa exponentialgrowthofpositiveinitialenergyforasystemofhigherorderviscoelasticwaveequationswithvariableexponents AT salahboulaaras exponentialgrowthofpositiveinitialenergyforasystemofhigherorderviscoelasticwaveequationswithvariableexponents |