Arrieta Algarra, José MaríaFerreira de Pablo, RaúlPablo, Arturo deRossi, Julio D.2023-06-202023-06-2020101553-523110.3934/dcds.2009.26.43https://hdl.handle.net/20.500.14352/42005In this paper we prove a general result concerning continuity of the blow-up time and the blow-up set for an evolution problem under perturbations. This result is based on some convergence of the perturbations for times smaller than the blow-up time of the unperturbed problem together with uniform bounds on the blow-up rates of the perturbed problems. We also present several examples. Among them we consider changing the special domain in which the heat equation with a power source takes place. We consider rather general perturbations of the domain and show the continuity of the blow- up time. Moreover, we deal with perturbations on the initial condition and on parameters in the equation. Finally, we also present some continuity results for the blow-up setengjournal articlehttp://www.aimsciences.org/journals/home.jsp?journalID=1open access517.98StabilityBlow-upPerturbationsPerturbations of the domainPerturbations of parametersBlow-up ratesPerturbations on the initial conditionAnálisis funcional y teoría de operadores