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.
Coupled Kirchhoff beam system, logarithmic source, global solutions, exponential stability
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