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math.AP2023
Local solvability and dilation-critical singularities of supercritical fractional heat equations
Yohei Fujishima, Kotaro Hisa, Kazuhiro Ishige +1
We consider the Cauchy problem for fractional semilinear heat equations with supercritical nonlinearities and establish both necessary conditions and sufficient conditions for loca…
math.AP2023★ 2 cited
A general nonlinear characterization of stochastic incompleteness
Gabriele Grillo, Kazuhiro Ishige, Matteo Muratori +1
Stochastic incompleteness of a Riemannian manifold amounts to the nonconservation of probability for the heat semigroup on . We show that this property is equivalent to the…