| Abstract: |
| We study integrability conditions for existence and nonexistence of a local-in-time integral solution of fractional semilinear heat equations with rather general growing nonlinearities in uniformly local Lebesgue spaces.
We introduce a new supersolution which plays a crucial role.
Our method does not rely on a change of variables, and hence it can be applied to a wide class of nonlocal parabolic equations.
In particular, when the nonlinear term is a pure power or pure exponential function, a local-in-time solution can be constructed in the critical case, and integrability conditions for the existence and nonexistence are completely classified.
Our analysis is based on the comparison principle, Jensen`s inequality and the smoothing effect. |
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