Existence of self-similar finite-mass solutions is proved for the time-fractional porous-medium equation in the optimal range m > (d-2)_+/d for all d ≥ 1, with compact support for m > 1 and heavy tails for m_c < m < 1.
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Existence, uniqueness, and positivity-preserving properties are established for a non-local singular non-linear Fokker-Planck PDE and its corresponding McKean SDE.
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Self-similar solutions to the time-fractional Porous-Medium Equation
Existence of self-similar finite-mass solutions is proved for the time-fractional porous-medium equation in the optimal range m > (d-2)_+/d for all d ≥ 1, with compact support for m > 1 and heavy tails for m_c < m < 1.
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A non-local singular non-linear Fokker-Planck PDE
Existence, uniqueness, and positivity-preserving properties are established for a non-local singular non-linear Fokker-Planck PDE and its corresponding McKean SDE.