Abstract
We study the class of non-negative continuous weak solutions of the Generalized Porous Medium equations
\(\frac{{\partial u}} {{\partial t}} = \Delta \phi \left( {x,t,u} \right), \left( {x,t} \right) \in \mathbb{R}^n \times \left( {0,T} \right), \)
where n ≥ 1 and 0 < T ≤ ∞. We give a complete description of solutions in terms of existence, uniqueness, existence of initial trace and blow up.
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Daskalopoulos, P. The Cauchy Problem for Variable Coefficient Porous Medium Equations. Potential Analysis 7, 485–516 (1997). https://doi.org/10.1023/A:1017967218024
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DOI: https://doi.org/10.1023/A:1017967218024