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Session

PDE3: Partial Differential Equations Location: G227 Session Chair: Simon Markfelder Session Chair: Marlies Pirner

Presentation 4

Finite propagation speed for Leibenson’s equation on Riemannian manifolds Philipp Sürig Bielefeld University, Germany We consider on arbitrary Riemannian manifolds the Leibenson equation \begin{equation*} \partial _{t}u=\Delta _{p}u^{q}. \end{equation*} This equation is also known as doubly nonlinear evolution equation. It comes from hydrodynamics where it describes filtration of a turbulent compressible liquid in porous medium. We show that, under optimal restrictions on $p$ and $q$, non-negative bounded solutions to this equation have finite propagation speed. The talk is based on joint work with Alexander Grigor'yan.