Filippas, StathisHerrero, Miguel A.Velázquez, J.J. L.2023-06-202023-06-2020001364-502110.1098/rspa.2000.0648https://hdl.handle.net/20.500.14352/57582We consider the semilinear heat equation with critical power nonlinearity. Using formal. arguments based on matched asymptotic expansion techniques, we give a detailed description of radially symmetric sign-changing solutions, which blow-up at x = 0 and t = T < ∞, for space dimension N = 3,4,5,6. These solutions exhibit fast blow-up; i.e. they satisfy lim(t up arrowT)(T - t)(1/(p-1))u(0, t) = ∞. In contrast, radial solutions that are positive and decreasing behave as in the subcritical case for any N ≥ 3. This last result is extended in the case of exponential nonlinearity and N = 2.engjournal articlehttp://rspa.royalsocietypublishing.org/content/456/2004/2957.full.pdf+htmlhttp://rspa.royalsocietypublishing.orgrestricted access536.2517.956.4Matched asymptotic expansionssemilinear heat equationblow-upcritical exponentssingularitiesdynamicsEcuaciones diferenciales1202.07 Ecuaciones en Diferencias