Global weak solutions with explicit L∞ decay are shown to exist for u_t = Δ_p u^m + u^q on complete non-compact manifolds with Sobolev (and possibly Poincaré) inequalities, for small initial data and q above a critical exponent.
Barenblatt, On self-similar motions of a compressible fluid in a porous medium , Akad
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Global existence for a Leibenson type equation with reaction on Riemannian manifolds
Global weak solutions with explicit L∞ decay are shown to exist for u_t = Δ_p u^m + u^q on complete non-compact manifolds with Sobolev (and possibly Poincaré) inequalities, for small initial data and q above a critical exponent.