Global Existence and Blow-up for Semilinear Wave Equations with Variable Coefficients |
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Authors: | Qian LEI and Han YANG |
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Affiliation: | 1.School of Mathematics,Southwest Jiaotong University,Chengdu,China;2.School of Mathematics,Southwest Jiaotong University,Chengdu,China;3.School of Transportation and Logistics,Southwest Jiaotong University,Chengdu,China |
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Abstract: | The authors consider the critical exponent problem for the variable coefficients wave equation with a space dependent potential and source term. For sufficiently small data with compact support, if the power of nonlinearity is larger than the expected exponent, it is proved that there exists a global solution. Furthermore, the precise decay estimates for the energy, L2 and Lp+1 norms of solutions are also established. In addition, the blow-up of the solutions is proved for arbitrary initial data with compact support when the power of nonlinearity is less than some constant. |
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Keywords: | Semilinear wave equations Global existence Energy decay $L^2$ and $L^{p+1}$ estimates Blow up |
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