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- W2890619571 abstract "We consider a family of semilinear parabolic problems with nonlinear boundary conditions [ left{ begin{aligned} u_t(x,t) &=Delta u(x,t) -au(x,t) + f(u(x,t)), x in Omega_epsilon mbox{ and } displaystylefrac{partial u}{partial N}(x,t) &=g(u(x,t)), x in partialOmega_epsilon mbox{ and } t>0,, end{aligned} right. ] where $Omega_0 subset mathbb{R}^n$ is a smooth (at least $mathcal{C}^2$) domain , $Omega_{epsilon} = h_{epsilon}(Omega_0)$ and $h_{epsilon}$ is a family of diffeomorphisms converging to the identity in the $mathcal{C}^1$-norm. Assuming suitable regularity and dissipative conditions for the nonlinearites, we show that the problem is well posed for $epsilon>0$ sufficiently small in a suitable scale of fractional spaces, the associated semigroup has a global attractor $mathcal{A}_{epsilon}$ and the family ${mathcal{A}_{epsilon}}$ is continuous at $epsilon = 0$." @default.
- W2890619571 created "2018-09-27" @default.
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- W2890619571 date "2018-09-05" @default.
- W2890619571 modified "2023-10-16" @default.
- W2890619571 title "Continuity of attractors for $mathcal{C}^1$ perturbations of a smooth domain" @default.
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