Iagar, Razvan GabrielSánchez, Ariel2025-05-202025-05-202025-03-06Iagar RG, Sánchez A. A critical non-homogeneous heat equation with weighted source. European Journal of Applied Mathematics. Published online 2025:1-12. doi:10.1017/S095679252500004X0956-7925 (print)1469-4425 (online)https://hdl.handle.net/10115/86737Some qualitative properties of radially symmetric solutions to the non-homogeneous heat equation with critical density and weighted source |x|−2∂tu=Δu+|x|σup,(x,t)∈RN×(0,T), are obtained, in the range of exponents p>1 , σ≥−2 . More precisely, we establish conditions fulfilled by the initial data in order for the solutions to either blow-up in finite time or decay to zero as t→∞ and, in the latter case, we also deduce decay rates and large time behavior. In the limiting case σ=−2, we prove the existence of non-trivial, non-negative solutions, in stark contrast to the homogeneous case. A transformation to a generalized Fisher–KPP equation is derived and employed in order to deduce these properties.enAttribution-ShareAlike 4.0 Internationalhttp://creativecommons.org/licenses/by-sa/4.0/Non-homogeneous heat equationcritical densityreaction–diffusion equationscritical exponentsdecay ratefinite time blow-upArticle10.1017/S095679252500004Xinfo:eu-repo/semantics/openAccess