Quasilinear parabolic and elliptic equations with singular potentials (Q2001229)

The author considers quasilinear parabolic equations with a Hardy potential and gives the asymptotic behavior of the solutions. It has been proven that all the solutions have the same asymptotic behavior: they all tend to the solution of the original problem which satisfies a zero initial condition. Moreover, estimates on the ``distance'' between the solutions of the evolution problem and the solutions of elliptic problems have been investigated by showing that in many cases (as for example the autonomous case) these last solutions are ``good approximations'' of the solutions of the original parabolic PDE. For the entire collection see [Zbl 1411.37003].