The blowup for 2-D quasilinear wave equations with cubic nonlinearity |
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Authors: | Huicheng Yin |
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Institution: | Department of Mathematics, Nanjing University, Nanjing 210093, China |
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Abstract: | For 2-D quasilinear wave equations with cubic nonlinearity and small initial data, we not only show that the solutions blow up in finite time but also give a complete asymptotic expansion of the lifespan of classical solutions. Hence we solve a problem posed by S. Alinhac and A. Hoshiga. Moreover, as an application of this result, we prove the blowup of solutions for the nonlinear vibrating membrane equations. |
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Keywords: | lifespan blowup Goursat problem Nash-Moser iteration |
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