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.
Time-fractional gradient flows for nonconvex energies in Hilbert spaces
2 Pith papers cite this work. Polarity classification is still indexing.
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Establishes global existence and uniqueness of L¹-solutions to time-fractional nonlinear diffusion equations and shows mass conservation with no finite-time extinction for fast diffusion cases.
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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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Existence and uniqueness of $L^1$-solutions to time-fractional nonlinear diffusion equations
Establishes global existence and uniqueness of L¹-solutions to time-fractional nonlinear diffusion equations and shows mass conservation with no finite-time extinction for fast diffusion cases.