Existence,blow‐up,and exponential decay estimates for a system of nonlinear wave equations with nonlinear boundary conditions |
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Authors: | Le Thi Phuong Ngoc Nguyen Thanh Long |
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Institution: | 1. Nhatrang Educational College, , 01 Nguyen Chanh Str., Nhatrang City, Vietnam;2. Department of Mathematics and Computer Science, University of Natural Science, Vietnam National University, Ho Chi Minh City, , Ho Chi Minh City, Vietnam |
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Abstract: | This paper is devoted to the study of a system of nonlinear equations with nonlinear boundary conditions. First, on the basis of the Faedo–Galerkin method and standard arguments of density corresponding to the regularity of initial conditions, we establish two local existence theorems of weak solutions. Next, we prove that any weak solutions with negative initial energy will blow up in finite time. Finally, the exponential decay property of the global solution via the construction of a suitable Lyapunov functional is presented. Copyright © 2013 John Wiley & Sons, Ltd. |
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Keywords: | system of nonlinear equations Faedo– Galerkin method local existence global existence blow up exponential decay |
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