# Arturo de Pablo Martínez

## Scientific Publications in the last years

- Anisotropic nonlocal diffusion equations with singular forcing (with F. Quirós and A. Rodríguez), Submitted. Preprint. arxiv:1810.
07499 - Grow-up for a quasilinear heat equation with a localized reaction (with R. Ferreira), J. Differential Equations (to appear). Preprint arXiv:1801.09525
- Remarks on a nonlinear nonlocal operator in Orlicz spaces (with E. Correa), Adv. Nonlinear Anal. 9 (2020) 305–326.
- Grow-up for a quasilinear heat equation with a localized reaction in higher dimensions (with R. Ferreira), Rev. Mat. Complut. 31 (2018) 805-832.
- Regularity theory for singular nonlocal diffusion equations (with F. Quirós and A. Rodríguez), Calc. Var. Partial Differential Equations 57 (2018) 57:136.
- Nonlocal operators of order near zero J. Math. Anal. Appl 461 (2018), No1, 837-867.
- Nonlocal heat equations: regularizing effect, decay estimates and Nash inequalities (with C. Brändle), Commun. Pure Appl. Anal. 17 (2018), No. 3, 1161-1178.
- Classical solutions and higher regularity for nonlinear fractional diffusion equations (with F. Quirós, A. Rodríguez and J.L. Vazquez), J. Euro. Math. Soc. 19 (2017), N0. 7, 1949-1975.
- Nonlocal filtration with rough kernels (with F. Quirós and A. Rodríguez). Nonlinear Anal., 137 (2016), 402-425.
- Perturbations of a critical fractional equation (with E. Colorado and U. Sánchez) Pacific J. Math., 271 (2014), No. 1, 65–85.
- Classical solutions for a logarithmic fractional diffusion equation (with F. Quirós, A. Rodríguez and J.L. Vazquez), J. Math. Pure Appl., 101 (2014), no. 6, 901–924.
- A concave-convex elliptic problem involving the fractional Laplacian (with C. Brändle, E. Colorado and U. Sánchez), Proc. Roy. Soc. Edinburgh, 143 (2013), 39-71.
- The Cauchy problem for a nonhomogeneous heat equation with reaction (with G. Reyes and A. Sánchez), Discrete Contin. Dyn. Syst., 33 (2013), 643--662.
- A general fractional porous medium equation (with F. Quirós, A. Rodríguez and J.L. Vazquez), Comm. Pure Applied Math., 65 (2012), 1242--1284.
- On some critical problems for the fractional Laplacian operator (with B. Barrios, E. Colorado and U. Sánchez), J. Differential Equations, 252 (2012), 6133-6162.
- Critical exponents for a semilinear parabolic equation with variable reaction (with R. Ferreira, M. Pérez-Llanos and J.D. Rossi), Proc. Roy. Soc. Edinburgh, 142 (2012), 1027--1042.
- A fractional porous medium equation (with F. Quirós, A. Rodríguez and J.L. Vázquez), Adv. Math. 226 (2011) 1378–1409.
- Stability of the blow-up time and the blow-up set under perturbations (with J.M. Arrieta, R. Ferreira and J.D. Rossi), Discrete Contin. Dyn. Syst. 26 (2010), 43--6.
- Critical coefficients in blow-up problems. Dynam. Systems Appl. 18 (2009), 81--102.
- Incomplete quenching in a system of heat equations coupled at the boundary (with R. Ferreira, M. Pérez-Llanos and J.D. Rossi). J. Math. Anal. Appl. 346 (2008), 145--154.
- Blow-up for a heat equation with convection and boundary flux (with G. Reyes and A. Sánchez). Proc. Roy. Soc. Edinburgh Sect A 138 (2008), 513--530.
- Blow-up with logarithmic nonlinearities (with R. Ferreira and J.D. Rossi). J. Differential Equations 249 (2007), 196--215.
- Classification of blow-up with nonlinear diffusion and localized reaction (with R. Ferreira nad J.L. Vázquez). J. Differential Equations 231 (2006), 195--211.
- An introduction to the problem of blow-up for semilinear and quasilinear parabolic equations. MAT. Serie A 12 (2006).
- Non-simultaneous quenching in a system of heat equations coupled at the boundary (with R. Ferreira, F. Quirós and J.D. Rossi). Z. Angew. Math. Phys. 57 (2006), 586--594.
- Blow-up for a degenerate diffusion problem not in divergence form (with R. Ferreira and J.D. Rossi). Indiana Univ. Math. J. 55 (2006), 955--974.
- The interfaces of an inhomogeneous porous medium equation with convection (with R. Ferreira, G. Reyes and A. Sánchez). Comm. Partial Differential Equations 31 (2006), 497--514.
- Long time behaviour for a nonlinear first-order equation (with G. Reyes). Nonlinear Anal. 65 (2006), 284--300.