Publications

Preprints:

• Arrieta J. M., Ferreira R., & Junquera S. (2025) Quenching phenomena in a system of non-local diffusion equations. Available at arXiv:2503.23994.

• Ruiz-Cases, J. (2025) Fractional fast diffusion with initial data a Radon measure. Available at arXiv:2503.14296.

• Cañizo J. A., Gárriz A., & Quirós F. (2025). Large-time estimates for the Dirichlet heat equation in exterior domains. Available at arXiv:2503.01492.

• Ferreira, R., & del Teso, F. (2024) The Fujita exponent for finite difference approximations of nonlocal and local semilinear blow-up problems. Available at arXiv:2410.10458v2.

• del Pezzo, L. & Ferreira, R. Fujita exponent and blow-up rate for a mixed local and nonlocal heat equation. Available at arXiv:2408.01577 [math.AP].

• Ferreira, R., & de Pablo, A. (2024). Blow-up for a double nonlocal heat equation. Available at arXiv:2406.14428v1 [math.AP].

• Muratori, M., Petitt, T.; & Quirós, F. (2024). An inhomogeneous porous medium equation with non-integrable data: asymptotics. Available at arXiv:2403.12854v1 [math.AP]

• de Pablo, A., Quirós, F., Ruiz-Cases, J. (2024) Positivity and asymptotic behaviour of solutions to a generalized nonlocal fast diffusion equation. Available at arXiv:2403.06647.

• Cortázar, C., Quirós, F., & Wolanski, N. Decay/growth rates for inhomogeneous heat equations with memory. The case of small dimensions. Available at arXiv:2204.11342 [math.AP].

Recent publications:

• Gonzálvez, I., Miranda, A., Rossi, J., Ruiz-Cases, J. (2024). Finding the convex hull of a set using the flow by minimal curvature with an obstacle. A game theoretical approach. Comm. Anal. Geom., to appear. Available at arXiv:2409.06855 [math.AP].

• Cortázar, C., Quirós, F., & Wolanski, N. (2024). A semilinear problem associated to the space-time fractional heat equation in ℝᴺ. Calc. Var. Partial Differential Equations, to appear.  Available at arXiv: 2405.18612 [math.AP].

• Du, Y., Gárriz, A.; & Quirós, F. Precise travelling-wave behaviour in doubly nonlinear reaction-diffusion equations. To appear in J. Eur. Math. Soc. (JEMS). Available at arXiv:2009.12959 [math.AP].

• Rossi, J., Ruiz-Cases, J. (2024). The trace fractional Laplacian and the mid-range fractional Laplacian. Nonlinear Anal, 247, Paper No. 113605, 24pp. Available at arXiv:2309.11621.

• Endal, J., Ignat, L., & Quirós, F. (2024). Heat equations with fast convection: Source-type solutions and large-time behaviour. Discrete Contin. Dyn. Syst. Ser. S 17 (2024), no. 4, 1497–1512. 

• Gonzálvez, I., Miranda, A., & Rossi, J. (2024).  Monotone iterations of two obstacle problems with different operators. Journal of Elliptic and Parabolic Equations.

• Cortázar, C., Quirós, F., & Wolanski, N. Asymptotic profiles for inhomogeneous heat equations with memory. Math. Ann., 389, 3705–3746 (2024). Available at arXiv:2302.10251 [math.AP].

• Audrito, A., Gárriz, A., & Quirós, F. (2024) Convergence in relative error for the porous medium equation in a tube. Ann. Mat. Pura Appl. (4) 203 (2024), no. 1, 149–171.

• Ferreira, R., & de Pablo, A. (2024). Blow-up for a fully fractional heat equation. Discrete Contin. Dyn. Syst., 44(2), 569–584.

• Endal, J., Ignat, L., & Quirós, F. (2023). Large-time behaviour for anisotropic stable nonlocal diffusion problems with convection. J. Math. Pures Appl. (9), 179, 277–336.

• Gárriz, A. (2023) Singular integral equations with applications to travelling waves for doubly nonlinear diffusion. J. Evol. Equ. 23, no. 3, Paper No. 54, 41 pp. 

• Pezzo, L., & Ferreira, R. (2023). Non-simultaneous blow-up for a system with local and non-local diffusion. J. Evol. Equ., 23(3), Paper No. 48, 14.

• Loeper, G., & Quirós, F. (2023). Interior second derivatives estimates for nonlinear diffusions. Discrete Contin. Dyn. Syst., 43(3-4), 1547–1559.

• de Pablo, A., Quirós, F., & Ritorto, A. (2022). Extremals in Hardy-Littlewood-Sobolev inequalities for stable processes. J. Math. Anal. Appl., 507(1), Paper No. 125742, 18.

• Ferreira, R., & de Pablo, A. (2022). A nonlinear diffusion equation with reaction localized in the half-line. Math. Eng., 4(3), Paper No. 024, 24.

• Cortázar, C., Quirós, F., & Wolanski, N. (2022). Decay/growth rates for inhomogeneous heat equations with memory. The case of large dimensions. Math. Eng., 4(3), Paper No. 022, 17.

• Gárriz, A.; Ignat, L. I.  (2021) A non-local coupling model involving three fractional Laplacians. Bull. Math. Sci. 11, no. 2, Paper No. 2150007, 35 pp. 

• Cortázar, C., Quirós, F., & Wolanski, N. (2021). Large-time behavior for a fully nonlocal heat equation. Vietnam J. Math., 49(3), 831–844.

• Cortázar, C., Quirós, F., & Wolanski, N. (2021). A heat equation with memory: large-time behavior. J. Funct. Anal., 281(9), Paper No. 109174, 40.

• Ferreira, R., & de Pablo, A. (2021). Blow-up rates for a fractional heat equation. Proc. Amer. Math. Soc., 149(5), 2011–2018.

• Gárriz, A.  (2020) Propagation of solutions of the Porous Medium Equation with reaction and their travelling wave behaviour. Nonlinear Anal. 195, 111736, 23 pp. 

• de Pablo, A., Quirós, F., & Rodríguez, A. (2020). Anisotropic nonlocal diffusion equations with singular forcing. Ann. Inst. H. Poincaré C Anal. Non Linéaire, 37(5), 1167–1183.

• Gárriz, A., Quirós, F., & Rossi, J. (2020). Coupling local and nonlocal evolution equations. Calc. Var. Partial Differential Equations, 59(4), Paper No. 112, 24.

• Du, Y., Quirós, F., & Zhou, M. (2020). Logarithmic corrections in Fisher-KPP type porous medium equations. J. Math. Pures Appl. (9), 136, 415–455.

• Ferreira, R., & de Pablo, A. (2020). Grow-up for a quasilinear heat equation with a localized reaction. J. Differential Equations, 268(10), 6211–6229.

• Correa, E., & de Pablo, A. (2020). Remarks on a nonlinear nonlocal operator in Orlicz spaces. Adv. Nonlinear Anal., 9(1), 305–326.

• Cortázar, C., Quirós, F., & Wolanski, N. (2019). A nonlocal diffusion problem with a sharp free boundary. Interfaces Free Bound., 21(4), 441–462.

• Del Pezzo, L., Ferreira, R., & Rossi, J. (2019). Eigenvalues for a combination between local and nonlocal p-Laplacians. Fract. Calc. Appl. Anal., 22(5), 1414–1436.

• Ferreira, R. (2019). Blow-up for a semilinear non-local diffusion system. Nonlinear Anal., 189, 111564, 12.

• Ferreira, R., & de Pablo, A. (2018). Grow-up for a quasilinear heat equation with a localized reaction in higher dimensions. Rev. Mat. Complut., 31(3), 805–832.

• de Pablo, A., Quirós, F., & Rodríguez, A. (2018). Regularity theory for singular nonlocal diffusion equations. Calc. Var. Partial Differential Equations, 57(5), Paper No. 136, 14.

• Cortázar, C., Quirós, F., & Wolanski, N. (2018) Near-field asymptotics for the porous medium equation in exterior domains. The critical two-dimensional case. SIAM J. Math. Anal. 50, no. 3, 2664–2680. 

• Brändle, C., & de Pablo, A. (2018) Nonlocal heat equations: regularizing effect, decay estimates and Nash inequalities. Commun. Pure Appl. Anal. 17, no. 3, 1161–1178. 

• Correa, E.; de Pablo, A. (2018) Nonlocal operators of order near zero. J. Math. Anal. Appl. 461, no. 1, 837–867.

• Ferreira, R. (2018) Blow-up for a semilinear heat equation with moving nonlinear reaction. Electron. J. Differential Equations, Paper No. 32, 11 pp.

Highlighted publications:

• Brändle, C., Colorado, E., de Pablo, A., & Sánchez, U. (2013). A concave-convex elliptic problem involving the fractional Laplacian. Proc. Roy. Soc. Edinburgh Sect. A, 143(1), 39–71.

• Barrios, B., Colorado, E., de Pablo, A., & Sanchez, U. (2012). On some critical problems for the fractional Laplacian operator. J. Differential Equations, 252(11), 6133–6162.

• de Pablo, A., Quirós, F., Rodríguez, A., & Vázquez, J. (2012). A general fractional porous medium equation. Comm. Pure Appl. Math., 65(9), 1242–1284.

• de Pablo, A., Quirós, F., Rodríguez, A., & Vázquez, J. (2011). A fractional porous medium equation. Adv. Math., 226(2), 1378–1409.

• Perthame, B., Quirós, F., & Vázquez, J. (2014). The Hele-Shaw asymptotics for mechanical models of tumor growth. Arch. Ration. Mech. Anal., 212(1), 93–127.

• de Pablo, A., & Vázquez, J. (1991). Travelling waves and finite propagation in a reaction-diffusion equation. J. Differential Equations, 93(1), 19–61.

• Quirós, F., & Rossi, J. (2001). Blow-up sets and Fujita type curves for a degenerate parabolic system with nonlinear boundary conditions. Indiana Univ. Math. J., 50(1), 629–654.

• Quirós, F., & Rossi, J. (2001). Non-simultaneous blow-up in a semilinear parabolic system. Z. Angew. Math. Phys., 52(2), 342–346.

• Ferreira, R., & Bernis, F. (1997). Source-type solutions to thin-film equations in higher dimensions. European J. Appl. Math., 8(5), 507–524.

• Ferreira, R., de Pablo, A., Pérez-LLanos, M., & Rossi, J. (2012). Critical exponents for a semilinear parabolic equation with variable reaction. Proc. Roy. Soc. Edinburgh Sect. A, 142(5), 1027–1042.