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Global existence and asymptotic behavior of small solutions for semilinear dissipative wave equations

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  • We study the global existence and asymptotic behavior of solutions to the Cauchy problem for the semilinear dissipative wave equations: $\square u + \partial_t u = |u|^{\alpha+1}$, $u|_{t=0}=\varepsilon u_0 \in H^1 \cap L^1$, $\partial_t u |_{t=0} = \varepsilon u_1 \in L^2 \cap L^1$ with a small parameter $\varepsilon>0$. When $N\le 3$ and $2/N<\alpha \le 2/[N-2]^+$, we show the global solvability and derive the sharp rates of the solutions.
    Mathematics Subject Classification: 35L15, 35L70, 35L05, 35B40.


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