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http://dx.doi.org/10.5666/KMJ.2021.61.4.859

Existence, Blow-up and Exponential Decay Estimates for the Nonlinear Kirchhoff-Carrier Wave Equation in an Annular with Robin-Dirichlet Conditions  

Ngoc, Le Thi Phuong (University of Khanh Hoa)
Son, Le Huu Ky (University of Science, Ho Chi Minh City, Vietnam National University, Faculty of Applied Sciences, Ho Chi Minh City University of Food Industry)
Long, Nguyen Than (Department of Mathematics and Computer Science, University of Science, Ho Chi Minh City)
Publication Information
Kyungpook Mathematical Journal / v.61, no.4, 2021 , pp. 859-888 More about this Journal
Abstract
This paper is devoted to the study of a nonlinear Kirchhoff-Carrier wave equation in an annulus associated with Robin-Dirichlet conditions. At first, by applying the Faedo-Galerkin method, we prove existence and uniqueness results. Then, by constructing a Lyapunov functional, we prove a blow up result for solutions with a negative initial energy and establish a sufficient condition to obtain the exponential decay of weak solutions.
Keywords
Nonlinear Kirchhoff-Carrier wave equation; Blow-up; Exponential decay;
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