This paper deals with the global solutions and exponential stability for a coupled system of Kirchhoff beam weakly damping and with a logarithmic source. We apply the potential well and establish the global well-posedness by using the Faedo--Galerkin approximations, taking into account that the initial data is located in a suitable set of stability created from the Nehari manifold. Moreover, by using Nakao's lemma, we prove the exponential stability of the solution.
PEREIRA, DUCIVAL CARVALHO; CUNHA, CARLOS ALBERTO RAPOSO DA; and CATTAI, ADRIANO PEDREIRA
"Global existence and energy decay for a coupled system of Kirchhoff beam equations with weakly damping and logarithmic source,"
Turkish Journal of Mathematics: Vol. 46:
2, Article 10.
Available at: https://journals.tubitak.gov.tr/math/vol46/iss2/10