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
Abstract:
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
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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
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Le Thi Phuong Ngoc
University of Khanh Hoa
01 Nguyen Chanh Str.,
Nha Trang City, Vietnam
email: ngoc1966@gmail.com
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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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