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Published in:
2019 | OriginalPaper | Chapter
Quasilinear Parabolic and Elliptic Equations with Singular Potentials
Author : Maria Michaela Porzio
Published in: 2017 MATRIX Annals
Publisher: Springer International Publishing
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In this paper we describe the asymptotic behavior of the solutions to quasilinear parabolic equations with a Hardy potential. We prove 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, we derive estimates on the “distance” between the solutions of the evolution problem and the solutions of elliptic problems 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.