| Abstract: |
| This talk investigates the regular solutions and the stability of strong attractors for a class of semilinear wave equations with gentle dissipation in $\Omega\subset \r^3$:
$u_{tt}-\Delta u+\gamma (-\Delta)^\theta u_t +f(u)=g(x)$, with dissipative index $\theta \in (0, 1/2)$. It shows that when the growth exponent $p$ of the nonlinearity $f(u)$ is up to the range: $1\leq p0$; (ii) for each $\theta\in (0, 1/2)$, the related solution semigroup has in natural energy space a strong global attractor $\mathcal{A}_\theta$ and a strong exponential attractor $\mathcal {E}^\theta$, whose compactness, attraction property and boundedness of fractal dimension are in the strong solution space; (iii) the family of global attractors and exponenial attractors are stable with respect to the dissipative index $\theta \in (0, 1/2)$. |
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