Hernández-Bermejo, BenitoIagar, Razvan GGordoa, Pilar RPickering, AndrewSánchez, Ariel2024-12-022024-12-022020J. Math. Anal. Appl. 482 (2020) 123503Benito Hernández-Bermejo, Razvan Gabriel Iagar, Pilar R. Gordoa, Andrew Pickering, Ariel Sánchez, Equivalence and finite time blow-up of solutions and interfaces for two nonlinear diffusion equations, Journal of Mathematical Analysis and Applications, Volume 482, Issue 1, 2020, 123503, ISSN 0022-247X, https://doi.org/10.1016/j.jmaa.2019.1235030022-247Xhttps://hdl.handle.net/10115/42250B. H.-B. acknowledges Ministerio de Economía, Industria y Competitividad for grants MTM2017-84383-P and MTM2016-80276-P. The work of P. R. G. and A. P. is supported by the Ministry of Economy and Competitiveness of Spain under contract MTM2016-80276-P (AEI/FEDER, EU). The work of A. S. is partially supported by the Spanish project MTM2017-87596-P.In this work, we construct a transformation between the solutions to the following reaction-convection-diffusion equation u_t = (u^m)_{xx} + a(x)(u^m)_x + b(x)u^m, posed for x ∈ R, t ≥ 0 and m > 1, where a, b are two continuous real functions, and the solutions to the nonhomogeneous diffusion equation of porous medium type f(y)θ_τ = (θ^m)_{yy}, posed in the half-line y ∈ [0, ∞) with τ ≥ 0, m > 1 and suitable density functions f(y). We apply this correspondence to the case of constant coefficients a(x) = 1 and b(x) = K > 0. For this case, we prove that compactly supported solutions to the first equation blow up in finite time, together with their interfaces, as x → −∞. We then establish the large time behavior of solutions to a homogeneous Dirichlet problem associated to the first equation on a bounded interval. We also prove a finite time blow-up of the interfaces for compactly supported solutions to the second equation when f(y) = y^{−γ} with γ > 2.engAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/reaction-convection-diffusion equationsnonhomogeneous equationsfinite time blow-upporous medium equationcorrespondence of solutionsinfo:eu-repo/semantics/article10.1016/j.jmaa.2019.123503info:eu-repo/semantics/openAccess