The paper proves short-time existence, uniqueness and maximal L^q-regularity for the fractional porous medium equation on manifolds with conical singularities, and gives the decay rate of solutions near the conical tips.
Global solutions to the Porous medium equations on singular manifolds
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abstract
The main objective of the present work is to discuss the global existence and stability of solutions to the porous medium equations on Riemannian manifolds with singularities. Several different types of solutions are considered. Our proof is based on a Poincare inequality on function space defined on manifolds with singularities.
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2019 1verdicts
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The fractional porous medium equation on manifolds with conical singularities I
The paper proves short-time existence, uniqueness and maximal L^q-regularity for the fractional porous medium equation on manifolds with conical singularities, and gives the decay rate of solutions near the conical tips.