| Abstract: |
| We consider a priori estimates of possibly sign-changing solutions
to superlinear parabolic problems and their applications (blow-up rates,
continuity of the blow-up time, existence of nontrivial steady states etc.).
Our estimates are based on energy, interpolation and bootstrap arguments.
We first discuss known results on local problems and then provide new results
for problems with nonlocal nonlinearities or nonlocal differential operators.
In particular, we deal with nonlocal nonlinearities occuring
in the Choquard equation or the Schr\odinger-Poisson-Slater problem,
and we also consider problems involving the fractional Laplacian. |
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