Solutions of Kirchhoff plate equations with internal damping and logarithmic nonlinearity
| dc.contributor.author | Pereira, Ducival C. | |
| dc.contributor.author | Cordeiro, Sebastiao | |
| dc.contributor.author | Raposo, Carlos Alberto | |
| dc.contributor.author | Maranhao, Celsa | |
| dc.date.accessioned | 2021-08-23T13:30:31Z | |
| dc.date.available | 2021-08-23T13:30:31Z | |
| dc.date.issued | 2021-03-29 | |
| dc.description.abstract | In this article we study the existence of weak solutions for the nonlinear initial boundary value problem of the Kirchhoff equation utt + Δ2u + M(∥∇u∥2) (-Δu) + ut = u ln |u|2, in Ω x (0, T), u(x, 0) = u0(x), ut(x, 0) = u1(x), x ∈ Ω, u(x, t) = ∂u/∂η (x, t) = 0, x ∈ ∂Ω, t ≥ 0, where Ω is a bounded domain in ℝ2 with smooth boundary ∂Ω, T > 0 is a fixed but arbitrary real number, M(s) is a continuous function on [0, +∞) and η is the unit outward normal on ∂Ω. Our results are obtained using the Galerkin method, compactness approach, potential well corresponding to the logarithmic nonlinearity, and the energy estimates due to Nakao. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 14 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Pereira, D., Cordeiro, S., Raposo, C., & Maranhão, C. (2021). Solutions of Kirchhoff plate equations with internal damping and logarithmic nonlinearity. <i>Electronic Journal of Differential Equations, 2021</i>(21), pp. 1-14. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/14418 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2021, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Extensible beam | |
| dc.subject | Existence of solutions | |
| dc.subject | Asymptotic behavior | |
| dc.subject | Logarithmic source term | |
| dc.title | Solutions of Kirchhoff plate equations with internal damping and logarithmic nonlinearity | |
| dc.type | Article |