Electron. J. Differential Equations, Vol. 2021 (2021), No. 21, pp. 1-14.

Solutions of Kirchhoff plate equations with internal damping and logarithmic nonlinearity

Ducival Pereira, Sebastiao Cordeiro, Carlos Raposo, Celsa Maranhao

In this article we study the existence of weak solutions for the nonlinear initial boundary value problem of the Kirchhoff equation

where Ω is a bounded domain in R2 with smooth boundary $\partial \Omega$, T>0 is a fixed but arbitrary real number, M(s) is a continuous function on $[0,+\infty)$ and η is the unit outward normal on $\partial \Omega$. Our results are obtained using the Galerkin method, compactness approach, potential well corresponding to the logarithmic nonlinearity, and the energy estimates due to Nakao.

Submitted May 19, 2020. Published March 29, 2021.
Math Subject Classifications: 35L15, 35L70, 35B40, 35A01
Key Words: Extensible beam; existence of solutions; asymptotic behavior; logarithmic source term.
DOI: https://doi.org/10.58997/ejde.2021.21

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Ducival Pereira
Department of Mathematics
State University of Pará
Belém, PA 66113-200, Brazil
email: ducival@uepa.br
Sebastião Cordeiro
Faculty of Exact Sciences and Technology
Federal University of Pará
Abaetetuba, PA 68440-000, Brazil
email: sebastiao@ufpa.br
Carlos Raposo
Department of Mathematics
Federal University of São João del-Rei
São João del-Rei, MG 36307-352, Brazil
email: raposo@ufsj.edu.br
Celsa Maranhão
Department of Mathematics
Federal University of Pará
Belém, PA 66075-110, Brazil
email: celsa@ufpa.br

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