2026-06-28T10:38:32Zhttps://docta.ucm.es/rest/oai/request

oai:docta.ucm.es:20.500.14352/503242023-08-25T11:33:43Zcom_20.500.14352_14col_20.500.14352_15

Localization on the boundary of blow-up for reaction-diffusion equations with nonlinear boundary conditions. Arrieta Algarra, José María Rodríguez Bernal, Aníbal In this work we analyze the existence of solutions that blow-up in finite time for a reaction-diffusion equation ut−Δu=f(x,u) in a smooth domain Ω with nonlinear boundary conditions ∂u∂n=g(x,u). We show that, if locally around some point of the boundary, we have f(x,u)=−βup,β≥0, and g(x,u)=uq, then blow-up in finite time occurs if 2q>p+1 or if 2q=p+1 and β<q. Moreover, if we denote by Tb the blow-up time, we show that a proper continuation of the blow-up solutions are pinned to the value infinity for some time interval [T,τ] with Tb≤T<τ. On the other hand, for the case f(x,u)=−βup, for all x and u, with β>0 and p>1, we show that blow-up occurs only on the boundary. 2023-06-20T09:45:59Z 2023-06-20T09:45:59Z 2004-07 journal article 0360-5302 10.1081/PDE-200033760 https://hdl.handle.net/20.500.14352/50324 http://www.tandfonline.com/doi/full/10.1081/PDE-200033760 http://www.tandfonline.com/ eng BFM2000-0798 restricted access Taylor & Francis