Sharpness on the Lower Bound of the Lifespan of Solutions to Nonlinear Wave Equations |
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| Authors: | Yi ZHOU and Wei HAN |
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| Affiliation: | 1. Nonlinear Mathematical Modeling and Methods Laboratory; Shanghai Key Laboratory for Contemporary Applied Mathematics; School of Mathematical Sciences, Fudan University, Shanghai 200433, China
2. School of Mathematical Sciences, Fudan University, Shanghai 200433, China; Department of Mathematics, North University of China, Taiyuan 030051, China |
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| Abstract: | This paper is devoted to proving the sharpness on the lower bound of the lifespan of classical solutions to general nonlinear wave equations with small initial data in the case n = 2 and cubic nonlinearity (see the results of T. T. Li and Y. M. Chen in 1992). For this purpose, the authors consider the following Cauchy problem: | $left{ begin{gathered} square u = left( {u_t } right)^3 , n = 2, hfill t = 0: u = 0, u_t = varepsilon gleft( x right), x in mathbb{R}^2 , hfill end{gathered} right.$left{ begin{gathered} square u = left( {u_t } right)^3 , n = 2, hfill t = 0: u = 0, u_t = varepsilon gleft( x right), x in mathbb{R}^2 , hfill end{gathered} right. |
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| Keywords: | Nonlinear wave equation Cauchy problem Lifespan |
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