# American Institute of Mathematical Sciences

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October  1995, 1(4): 503-520. doi: 10.3934/dcds.1995.1.503

## Breakdown of solutions to $\square u+u_t=|u|^{1+\alpha}$

 1 School of Mathematical Sciences, Fudan University, Han Dan Road 220, Shanghai 200433 2 Department of Mathematics, Fudan University, Key Laboratory of Mathematics for Nonlinear Sciences (Fudan University), Ministry of Education of China, Shanghai 200433, China

Received  November 1994 Published  August 1995

In the paper we give an upper bound for the life-span of the mild solution to the Cauchy problem for semilinear equations $\square u+u_t=|u|^{1+\alpha}$ ($\alpha >0,$ constant) with certain small initial data. This shows the sharpness of the lower bound obtained in [2] on the life-span of classical solutions to the Cauchy problem for fully nonlinear wave equations with linear dissipation with small initial data.
Citation: Tatsien Li, Yi Zhou. Breakdown of solutions to $\square u+u_t=|u|^{1+\alpha}$. Discrete & Continuous Dynamical Systems - A, 1995, 1 (4) : 503-520. doi: 10.3934/dcds.1995.1.503
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