Global and blow-up solutions for a quasilinear hyperbolic equation with strong damping |
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Authors: | Fuqin Sun Mingxin Wang |
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Institution: | a School of Science, Tianjin University of Technology and Education, Tianjin 300222, PR China b Department of Mathematics, Southeast University, Nanjing 210096, PR China |
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Abstract: | In this paper, we study a quasilinear hyperbolic equation with strong damping. Firstly, by use of the successive approximation method and a series of classical estimates, we prove the local existence and uniqueness of a weak solution. Secondly, via some inequalities, the potential method and the concave method, we derive the asymptotic and blow-up behavior of the weak solution with different conditions. |
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Keywords: | 35L15 35L20 35L70 |
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