Arrieta Algarra, José MaríaRodríguez Bernal, Aníbal2023-06-202023-06-202004-100219-199710.1142/S0219199704001495https://hdl.handle.net/20.500.14352/50296In this paper we show that several known critical exponents for nonlinear parabolic problems axe optimal in the sense that supercritical problems are ill posed in a strong sense. We also give an answer to an open problem proposed by Brezis and Cazenave in [9], concerning the behavior of the existence time for critical problems. Our results cover nonlinear heat equations including the case of nonlinear boundary conditions and weigthed spaces settings. In the latter case we show that in some cases the critical exponent is equal to one.engjournal articlehttp://www.worldscientific.com/doi/pdf/10.1142/S0219199704001495http://www.worldscientific.com/restricted access517.9Critical exponentsNon-well-posednessNonlinear heat equationsNonlinear boundary conditionsWeighted spaces proper minimal solutionsEcuaciones diferenciales1202.07 Ecuaciones en Diferencias