Electron. J. Differential Equations, Vol. 2018 (2018), No. 167, pp. 1-26.

Existence, blow-up and exponential decay for Kirchhoff-Love equations with Dirichlet conditions

Nguyen Anh Triet, Vo Thi Tuyet Mai, Le Thi Phuong Ngoc, Nguyen Thanh Long

The article concerns the initial boundary value problem for a nonlinear Kirchhoff-Love equation. First, by applying the Faedo-Galerkin, we prove existence and uniqueness of a solution. Next, by constructing Lyapunov functional, we prove a blow-up of the solution with a negative initial energy, and establish a sufficient condition for the exponential decay of weak solutions.

Submitted May 21, 2018. Published October 4, 2018.
Math Subject Classifications: 35L20, 35L70, 35Q74, 37B25.
Key Words: Nonlinear Kirchhoff-Love equation; blow-up; exponential decay

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Nguyen Anh Triet
Department of Mathematics, University of Architecture of Ho Chi Minh City
196 Pasteur Str., Dist. 3, Ho Chi Minh City, Vietnam
email: anhtriet1@gmail.com
Vo Thi Tuyet Mai
University of Natural Resources and Environment of Ho Chi Minh City
236B Le Van Sy Str., Ward 1, Tan Binh Dist.
Ho Chi Minh City, Vietnam
email: vttmai@hcmunre.edu.vn
Le Thi Phuong Ngoc
University of Khanh Hoa
01 Nguyen Chanh Str., Nha Trang City, Vietnam
email: ngoc1966@gmail.com
Nguyen Thanh Long
Department of Mathematics and Computer Science
VNUHCM - University of Science
227 Nguyen Van Cu Str., Dist. 5, Ho Chi Minh City, Vietnam
email: longnt2@gmail.com

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