Mercoledì 9 gennaio 2019, alle ore 16:00, presso l'aula 3014 dell’edificio U5 dell’Università di Milano - Bicocca
il dott. Marcello D'Abbicco (Università di Bari)
terrà un seminario dal titolo “Asymptotics and critical exponents for dissipative evolution equations"
Abstract. In this talk we will summarize some recent results about the asymptotic profile of the solution to the forward Cauchy problem for some dissipative evolution equations, of the general form
\[ \begin{cases}
A u_{tt} + B u + C u_t =0 & t\geq0, \ x\in\mathbb{R}^n,\\
u(0,x)=u_0(x)\,,\\
u_t(0,x)=u_1(x)\,,
\end{cases} \]
where $A$, $B$ and $C$ are suitable polynomials in $\Delta$. In particular, setting $A=Id$, we can consider wave $(B=-\Delta)$, Klein-Gordon ($B=Id-\Delta$) and beam/plate equations ($B=\Delta^2,\Delta^2-\Delta$) under different dissipative effects ($C=Id,-\Delta,Id-\Delta$). Setting $A=Id-\Delta$, we can study the plate equation with rotational inertia and the double dispersion equation ($B=\Delta^2-\Delta$, $C=-\Delta$).
We will discuss some applications to the study of global existence of small data solutions for problems with power nonlinearity $|u|^p$.