Sanchez, ArielIagar, Razvan Gabriel2024-02-072024-02-072020Razvan Gabriel Iagar, Ariel Sánchez, Instantaneous and finite time blow-up of solutions to a reaction-diffusion equation with Hardy-type singular potential, Journal of Mathematical Analysis and Applications, Volume 491, Issue 1, 2020, 124244, ISSN 0022-247X, https://doi.org/10.1016/j.jmaa.2020.1242440022-247Xhttps://hdl.handle.net/10115/29823We deal with radially symmetric solutions to the reaction-diffusion equation with Hardy-type singular potential ut = Δum + K |x|2 um, posed in RN × (0, T), in dimension N ≥ 3, where m > 1 and 0 <K< (N − 2)2/4. We prove that, in dependence of the initial condition u0 ∈ L∞(RN ) ∩ C(RN ), its solutions may either blow up instantaneously or blow up in finite time at the origin, thus developing a singularity at x = 0, but they can be continued globally in weak sense. The instantaneous blow-up occurs for example for any data u0 such that u0(0) > 0. The proofs are based on a transformation mapping solutions to our equation into solutions to a non-homogeneous porous medium equation.engAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Reaction-diffusion equations Hardy-type potential Instantaneous blow-up Non-homogeneous porous mediuminfo:eu-repo/semantics/article10.1016/j.jmaa.2020.124244info:eu-repo/semantics/openAccess