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In this paper, we show the backward uniqueness in time of solutions to nonlinear integro-differential systems with Neumann or Dirichlet boundary conditions. We also discuss reasonable physical interpretations for our conclusions.
We present some recent results on the blow-up behavior of solutions of heat equations with nonlocal nonlinearities. These results concern blow-up sets, rates and profiles. We then compare them with the corresponding results in the local case, and we show that the two types of problems exhibit "dual" blow-up behaviors.
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