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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2025-01-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13660-024-03250-x |
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| Summary: | 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. |
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| ISSN: | 1029-242X |