Large time behaviour of solutions to a class of non-autonomous, degenerate parabolic equations (Q711569)

Let \(\Omega\) be a bounded domain in \(\mathbb R^N\) with \(C^1\)-boundary. The authors consider the following problem \[ \begin{cases} u_t=\operatorname{div} A(x,t,u,\nabla u), & (x,t)\in\Omega \times (t>0),\\ u(x,t)=0, & (x,t)\in \partial\Omega \times(t>0),\\ u(x,0)=u_0(x)\geq 0, & x\in\Omega, \end{cases} \] where \(u_0\in L^1(\Omega),\) \(\int_\Omega u_0(x)\,dx>0\) and the function \(A\) assumed to be only measurable and to satisfy suitable structural conditions. The asymptotic behavior of the solutions is studied proving that, even if the equation depends explicitly upon the time, several asymptotic properties, valid for the autonomous case, are preserved.