Stability Properties of Distributional Solutions for Nonlinear Viscoelastic Wave Equations with Variable Exponents
A system of nonlinear wave equations in viscoelasticity with variable exponents is considered. It is assumed that the kernel included in the integral term of the equations depends on both the time and the spatial variables. Using the Faedo–Galerkin method and the contraction mapping principle, a the...
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MDPI AG
2025-03-01
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| author | Mouhssin Bayoud Mohamed Karek Khaled Zennir Keltoum Bouhali Loay Alkhalifa |
| author_facet | Mouhssin Bayoud Mohamed Karek Khaled Zennir Keltoum Bouhali Loay Alkhalifa |
| author_sort | Mouhssin Bayoud |
| collection | DOAJ |
| description | A system of nonlinear wave equations in viscoelasticity with variable exponents is considered. It is assumed that the kernel included in the integral term of the equations depends on both the time and the spatial variables. Using the Faedo–Galerkin method and the contraction mapping principle, a theorem of unique solvability of the problem is proved. In addition, under appropriate variable assumptions, an estimate of the stability of the solution to the problem of determining the kernel is obtained. The study is based on Komornik’s inequality. We expand the class of nonlinear boundary value problems that can be investigated by well-known methods. |
| format | Article |
| id | doaj-art-3ebd3a7c5e974543a12e2c60baab3929 |
| institution | OA Journals |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-3ebd3a7c5e974543a12e2c60baab39292025-08-20T02:17:14ZengMDPI AGAxioms2075-16802025-03-0114424310.3390/axioms14040243Stability Properties of Distributional Solutions for Nonlinear Viscoelastic Wave Equations with Variable ExponentsMouhssin Bayoud0Mohamed Karek1Khaled Zennir2Keltoum Bouhali3Loay Alkhalifa4Department of Computer Science, University Center, El Cherif Bouchoucha-Aflou, Aflou-Laghouat P.O. Box 306, AlgeriaDepartment of Mathematics, College of Science, University of Kasdi Merbah, Ouargla 30000, AlgeriaDepartment of Mathematics, College of Science, Qassim University, Buraydah 52571, Saudi ArabiaDepartment of Mathematics, College of Science, Qassim University, Buraydah 52571, Saudi ArabiaDepartment of Mathematics, College of Science, Qassim University, Buraydah 52571, Saudi ArabiaA system of nonlinear wave equations in viscoelasticity with variable exponents is considered. It is assumed that the kernel included in the integral term of the equations depends on both the time and the spatial variables. Using the Faedo–Galerkin method and the contraction mapping principle, a theorem of unique solvability of the problem is proved. In addition, under appropriate variable assumptions, an estimate of the stability of the solution to the problem of determining the kernel is obtained. The study is based on Komornik’s inequality. We expand the class of nonlinear boundary value problems that can be investigated by well-known methods.https://www.mdpi.com/2075-1680/14/4/243variable exponentsnonlinear equationsweak solutionsviscoelasticKomornik’s inequality |
| spellingShingle | Mouhssin Bayoud Mohamed Karek Khaled Zennir Keltoum Bouhali Loay Alkhalifa Stability Properties of Distributional Solutions for Nonlinear Viscoelastic Wave Equations with Variable Exponents Axioms variable exponents nonlinear equations weak solutions viscoelastic Komornik’s inequality |
| title | Stability Properties of Distributional Solutions for Nonlinear Viscoelastic Wave Equations with Variable Exponents |
| title_full | Stability Properties of Distributional Solutions for Nonlinear Viscoelastic Wave Equations with Variable Exponents |
| title_fullStr | Stability Properties of Distributional Solutions for Nonlinear Viscoelastic Wave Equations with Variable Exponents |
| title_full_unstemmed | Stability Properties of Distributional Solutions for Nonlinear Viscoelastic Wave Equations with Variable Exponents |
| title_short | Stability Properties of Distributional Solutions for Nonlinear Viscoelastic Wave Equations with Variable Exponents |
| title_sort | stability properties of distributional solutions for nonlinear viscoelastic wave equations with variable exponents |
| topic | variable exponents nonlinear equations weak solutions viscoelastic Komornik’s inequality |
| url | https://www.mdpi.com/2075-1680/14/4/243 |
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