Existence,blow‐up,and exponential decay estimates for a system of semilinear wave equations associated with the helicalflows of Maxwell fluid |
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| Authors: | Le Thi Phuong Ngoc Cao Huu Hoa Nguyen Thanh Long |
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| Affiliation: | 1. Nha Trang Educational College, Nha Trang, Vietnam;2. Department of Fundamental Sciences, Tra Vinh University, Tra Vinh, Vietnam;3. 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: | The paper is devoted to the study of a system of semilinear wave equations associated with the helical flows of Maxwell fluid. First, based on 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, we give a sufficient condition to guarantee the global existence and exponential decay of weak solutions via the construction of a suitable Lyapunov functional. Copyright © 2015 John Wiley & Sons, Ltd. |
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| Keywords: | system of semilinear wave equations mixed nonhomogeneous conditions the helical flows of Maxwell fluid Faedo– Galerkin method blow‐up in finite time exponential decay subclass 35A01 35A02 35A35 35B40 35B65 35D30 |
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