Stability of the Blow-up Time and the Blow-up Set under Perturbations Articles uri icon

publication date

  • January 2010

start page

  • 43

end page

  • 46


  • 1


  • 26

International Standard Serial Number (ISSN)

  • 1078-0947

Electronic International Standard Serial Number (EISSN)

  • 1553-5231


  • In 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 spacial 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 set.