Abstract
ABSTRACTThis work is concerned with the equation ∂tρ = Δxρm, m > 1, known as the porous medium equation. It shows stability of the pressure of solutions close to flat travelling wave fronts in the homogeneous Lipschitz sense that is in a way optimal for the treatment of the equation. This is the first result of this type and implies global regularity estimates for any number of derivatives of the pressure. Consequences include smoothness, analyticity in temporal and tangential directions, and analyticity of the interface between empty and occupied regions.
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