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Title Asymptotic structure of the attractor for processes on time-dependent spaces

Name Monica Conti
Country Italy
Email monica.conti@polimi.it
Co-Author(s) Vittorino Pata
Submit Time 2014-02-26 06:26:00
Special Session 2: Nonlinear evolution PDEs and interfaces in applied sciences
We compare the asymptotic structure of the time-dependent attractor $A_t$ generated by the partial differential equation $$\eps u_{tt}+ \alpha u_t-\Delta u+f(u)=g,$$ where the positive function $\eps=\eps(t)$ tends to zero as $t\to\infty$, with the global attractor $A_\infty$ of its formal limit $$\alpha u_t-\Delta u+f(u)=g.$$ We establish an abstract result and we apply it to the proof of the convergence $A_t\to A_\infty$.