Geodesic
Existence and stability results of nonlinear higher-order wave equation with a nonlinear source term and a delay term
Mathematica Bohemica, Tome 148 (2023) no. 1, pp. 11-34
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We consider the initial-boundary value problem for a nonlinear higher-order nonlinear hyperbolic equation in a bounded domain. The existence of global weak solutions for this problem is established by using the potential well theory combined with Faedo-Galarkin method. We also established the asymptotic behavior of global solutions as $t\rightarrow \infty $ by applying the Lyapunov method.
We consider the initial-boundary value problem for a nonlinear higher-order nonlinear hyperbolic equation in a bounded domain. The existence of global weak solutions for this problem is established by using the potential well theory combined with Faedo-Galarkin method. We also established the asymptotic behavior of global solutions as $t\rightarrow \infty $ by applying the Lyapunov method.
DOI : 10.21136/MB.2022.0141-20
Classification : 35B40, 35L05, 35L75
Keywords: nonlinear higher-order hyperbolic equation; nonlinear source term; global existence 
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Abdelli, Mama; Beniani, Abderrahmane; Mezouar, Nadia; Chahtou, Ahmed. Existence and stability results of nonlinear higher-order wave equation with a nonlinear source term and a delay term. Mathematica Bohemica, Tome 148 (2023) no. 1, pp. 11-34. doi: 10.21136/MB.2022.0141-20

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