D. Bresch, P.-E. Jabin, J. Soler, A new approach to the mean-field limit of Vlasov-Fokker-Planck equations. preprint arXiv:2203.15747

P.-E. Jabin, D. Poyato, J. Soler, Mean field limit of non-exchangeable systems. preprint arXiv:2112.15406

J. Campos, C. García, J. Soler, Kinks and solitons in linear and nonlinear-diffusion Keller-Segel type models with logarithmic sensitivity, preprint arXiv:2102.13480

A. Aguirre-Tamaral, M. Cambón, D. Poyato, J. Soler, I. Guerrero, A guidance model predicting the role of Ihog-glypicans interaction in cytoneme orientation for Hedgehog signaling, preprint

Papers (inverse chronological order)


A. Béjar-López, C. Cunha, J. Soler, Two-dimensional incompressible micropolar fluids model with singular initial data, Physica D: Nonlinear Phenomena 430 (2022), 133069. Open Access

N. Bellomo, N. Outada, J. Soler, Y. Tao, M. Winkler, Chemotaxis and Cross-diffusion Models in Complex Environments: Models and Analytic Problems Towards a Multiscale Vision, Mathematical Models and Methods in Applied Sciences 32, No. 04 (2022), 713-792. Open Access


M. Conte, S. Casas-Tintò, J. Soler, Modeling invasion patterns in the glioblastoma battlefield, PLOS Computational Biology 17(1): e1008632, (2021) D.O.I. bioarXiv:10.1101/2020.06.17.156497

N. G. Corbin, C. Engwer, A. Klar, J. Nieto, J. Soler, C. Surulescu, M. Wenske, Modeling glioma invasion with anisotropy- and hypoxia-triggered motility enhancement: from subcellular dynamics to macroscopic PDEs with multiple taxis, Math. Mod. Meth. Appl. Sci. 31 (01) (2021), 177-222. D.O.I. arXiv:2006.12322

B. Blanco, J. Campos, J. Melchor, J. Soler, Modeling Interactions among Migration, Growth and Pressure in Tumor Dynamics, Mathematics 9: 1376, (2021) Open Access

J. Park, D. Poyato, J. Soler, Filippov trajectories and clustering in the Kuramoto model with singular couplings, Journal of the European Mathematical Society 23 (10) (2021), 3193–3278. D.O.I. arXiv:1809.04307

J. Kim, D. Poyato, J. Soler, Hydrodynamic limit of a coupled Cucker-Smale system with strong and weak internal variable relaxation, Math. Mod. Meth. Appl. Sci. 31 (06) (2021), 1163-1235. D.O.I. arXiv:2101.04585


C. García, T. Hmidi, J. Soler, Non uniform rotating vortices and periodic orbits for the two-dimensional Euler Equations, Archive for Rational Mechanics and Analysis 238 (2020), 929-1085. D.O.I. arXiv:1807.10017v2

J. Calvo, P. E. Jabin, J. Soler, Global weak solutions to the relativistic BGK equation, Communications in Partial Differential Equations 45:3 (2020), 191-229 D.O.I.

N. Bellomo, F. Brezzi, J. Soler, Recent results and challenges in behavioral systems, Math. Mod. Meth. Appl. Sci. 30 (10) (2020), 1857-1862. D.O.I.

N. Bellomo, F. Brezzi, J. Soler, Active particles methods and challenges in behavioral systems, Math. Mod. Meth. Appl. Sci. 30 (04) (2020), 653-658. D.O.I.


G. Albi, N. Bellomo, L. Fermo, S.-Y. Ha, J. Kim, L. Pareschi, D. Poyato, J. Soler, Vehicular traffic, crowds, and swarms. From kinetic theory and multiscale methods to applications and research perspectives, Math. Mod. Meth. Appl. Sci. 29 (10) (2019), 1901-2005. D.O.I.

J. Soler, Un mateix patró. In Vicent Caselles. Matemàtica i Passió. J. Bisquert Editor. Sito Editions (2019), 105-115. ISBN 978-84-947758-5-7.

N. A. Aguirre-Tamaral, M. Cambon, D. Poyato, J. Soler, I. Guerrero, , Modeling cytoneme guidance for Hedgehog signaling, European Biophysics Journal with Biophysics Letters 48 (2019), S54. Meeting Abstract.


A. Enciso, D. Poyato, J. Soler, Stability results, almost global generalized Beltrami fields and applications to vortex structures in the Euler equations, Comm. Math. Phys. 360 (2018), 197–269. D.O.I. arXiv:1605.06626

M. Arias, J. Campos, J. Soler, Cross-diffusion and traveling waves in porous-media flux-saturated Keller-Segel models, Math. Mod. Meth. Appl. Sci. 28 (11) (2018), 2103-2129 D.O.I. arXiv:1810.07606

I. Guerrero, J. Soler, ¿Hablan las células el lenguaje de las matemáticas?, El País. 27-08-2018 Link


D. Poyato, J. Soler, Euler-type equations and commutators in singular and hyperbolic limits of kinetic Cucker-Smale models, Math. Mod. Meth. Appl. Sci., 6 (2017), 1089–1152. D.O.I. arXiv:1611.00743

J. L. López, J. Soler, A space-time Wigner function approach to long time Schrödinger-Poisson dynamics, SIAM Mathematical Analysis 49(6) (2017), 4915-4941. D.O.I.

J. Calvo, J. Campos, V. Caselles, O. Sánchez, J. Soler, Qualitative behavior for flux-saturated mechanisms: traveling waves, waiting time and smoothing effects, Journal of the European Mathematical Society 19 (2017), 441-472. D.O.I. arXiv:1402.1679v2


J. Calvo, J. Campos, V. Caselles, O. Sánchez, J. Soler, Pattern formation in a flux limited reaction-diffusion equation of porous media type, Inventiones Mathematicae 206 (2016), 57–108.  D.O.I. arXiv:1309.6789

D. Poyato, J. Soler, Modeling social crowds, Physics of Life Reviews18 (2016), 50–52. D.O.I.

J. L. López, J. Soler, A non-Markovian phase space approach to Schrödinger dynamics: The space-time Wigner transform, SIAM-Multiscale Model. Simul. 14(1) (2016), 430-451. D.O.I.

J. Campos, J. Soler, Qualitative behavior and traveling waves for flux-saturated porous media equations arising in optimal mass transportation, Nonlinear Analysis TMA 137 (2016), 266-290. D.O.I.


N. Bellomo, F. Colasuonno, D. Knopoff, J. Soler, From a systems theory of sociology to modeling the onset and evolution of criminality, Networks and Heterogeneous Media 10(3), (2015), 421-441. D.O.I.

J. Calvo, J. Campos, V. Caselles, O. Sánchez, J. Soler, Flux-saturated porous media equations and applications, EMS Surveys in Mathematical Sciences 2(1), (2015), 131-218. D.O.I.

M.A. Herrero, J. Soler, Cooperation, competition, organization: The dynamics of interacting living populations, Math. Mod. Meth. Appl. Sci.  25(13) (2015), 2407-2415. D.O.I.

J.L. López, J. Soler, Mathematics and Biology: A round trip, comment on "On the Interplay between mathematics and biology: hallmarks toward a new systems biology", Phys. Life Rev. 12 (2015), 78-80. D.O.I.

O. Sánchez, J. Calvo, C. Ibanez, I. Guerrero, J. Soler, Modeling Hedgehog Signaling Through Flux-Saturated Mechanisms. In Hedgehog Signaling Protocols. N.A. Riobo, Editor. Methods in Molecular Biology, Vol. 1322 (2015), 9-33.


N. Bellomo, A. Bellouquid, J. Nieto, J. Soler, On the multiscale modeling of vehicular traffic: from kinetic to hydrodynamics, Discrete Contin. Dyn. Syst. Ser. B 19(7), (2014), 1869-1888. D.O.I.

J. Calvo, J. Nieto, J. Soler, M.O. Vásquez, On a dispersive model for the unzipping of double-stranded DNA molecules, Math. Mod. and Meth. in Appl. Sci. 24(3), (2014), 495-511. D.O.I.


N. Bellomo, A. Bellouquid, J. Nieto, J. Soler, Modeling chemotaxis from L2-closure moments in kinetic theory of active particles, Discrete Contin. Dyn. Syst. Ser. B 18(4), (2013), 847-863. D.O.I.

N. Bellomo, D. Knoppof, J. Soler, On the difficult interplay between life, "complexity", and mathematical sciences, Math. Mod. and Meth. in Appl. Sci. 23, (2013), 1861-1914. D.O.I.

A. Bellouquid, J. Calvo, J. Nieto, J. Soler, Hyperbolic vs parabolic asymptotics in kinetic theory towards fluid dynamic models, SIAM J. Appl. Math. 73(4), (2013), 1327-1346. D.O.I.

J. Campos, P. Guerrero, O. Sánchez, J. Soler, On the analysis of travelling waves to a nonlinear flux limited reaction-diffusion equation, Ann. Inst. H. Poincaré Anal. Non Linéaire30(1), (2013), 141-155. D.O.I.

I. Catto, J. Dolbeault, O. Sánchez, J. Soler, Existence of steady states for the Maxwell-Scrödinger-Poisson system: exploring the applicability of the concentration-compactness principle, Math. Mod. and Meth. in Appl. Sci. 23(10), (2013), 1915-1938.D.O.I.

J. Soler, Vicent Caselles, matemático, El País, 06-sept-2013

M. Verbeni, O. Sánchez, E. Mollica, I. Siegl-Cachedenier, A. Carleton, I. Guerrero, A. Ruiz i Altaba, J. Soler, Morphogenetic action through flux-limited spreading, Phys. Life Rev. 10, (2013), 457-475. D.O.I.

M. Verbeni, O. Sánchez, E. Mollica, I. Siegl-Cachedenier, A. Carleton, I. Guerrero, A. Ruiz i Altaba, J. Soler, On flux-limited morphogenesis: Reply to the comments on "Morphogenetic action through flux-limited spreading" Phys. Life Rev. 10, (2013), 495-497. D.O.I.


F. Andreu, J. Calvo, J.M. Mazón, J. Soler, On a nonlinear flux--limited equation arising in the transport of morphogens, J. Diff. Eq. 252(10), (2012), 5763--5813. D.O.I.

F. Andreu, V. Caselles, J.M. Mazón, J. Soler, M. Verbeni, Radially Symmetric Solutions of a Tempered Difusion Equation. A Porous Media, Flux-Limited Case, SIAM J. Math Anal. 44, (2012), 1019--1049. D.O.I.

N. Bellomo, A. Bellouquid, J. Nieto, J. Soler, On the asymptotic theory from microscopic to macroscopic growing tissue models: an overview with perspectives, Math. Mod. and Meth. in Appl. Sci. 22(1), (2012), 1130001 (37 pages) D.O.I.

N. Bellomo, J. Soler, On the mathematical theory of the dynamics of swarms viewed as complex systems, Math. Mod. and Meth. in Appl. Sci. 22, (2012), 1140006 (29 pages) D.O.I.

A. Bellouquid, J. Calvo, J. Nieto, J. Soler, On the relativistic BGK-Boltzmann model: asymptotics and hydrodynamics, J. Stat. Phys.149(2), (2012), 284--316. D.O.I.

X. Cabre, J. Soler (editors), Caffarelli L., Golse F., Guo Y., Kenig C., Vasseur A. (autors), Nonlinear Partial Differential Equations, Springer Basel (2012). ISBN 978-3-0348-0190-4


J. Calvo, J. Mazón, J. Soler, M. Verbeni, Qualitative properties of the solutions of a nonlinear flux-limited equation arising in the transport of morphogens, Math. Mod. and Meth. in Appl. Sci. 21(supp1), (2011), 893--937 . D.O.I.

Th. Goudon, J. Nieto, O. Sánchez, J. Soler, Vanishing viscosity regimes and non--standard shock relations for semiconductor superlattices models, SIAM J. Appl. Math. 71(1), (2011), 180--199. D.O.I.

J. SolerEn nuestras líneas de investigación establecemos relación con el mundo de la empresa y la experimentación, diario de edición nacional CincoDías, 23/feb/2011.

J. SolerLa UGR analiza la relación entre las matemáticas y las ciencias de la vida , diario IDEAL-Granada, 06/jun/2011.


N. Bellomo, A. Bellouquid, J. Nieto, J. Soler, Multiscale biological tissue models and flux-limited chemotaxis for multicellular growing systems, Math. Mod. and Meth. in Appl. 20 (7), (2010), 1179--1207. D.O.I.

N. Bellomo, A. Bellouquid, J. Nieto, J. Soler, Complexity and mathematical tools towards the modelling multicellular growing systems in Biology, Mathematical and Computing Modelling 51, (2010), 441--451 D.O.I.

S. Calogero, Calvo J., O. Sánchez, J. Soler, Virial inequalities for steady states in relativistic galactic dynamics, Nonlinearity23(8), (2010), 1851--1871 D.O.I.

S. Calogero, J. Calvo, O. Sánchez, J. Soler, Dispersive behavior in Galactic Dynamics, Discrete and Continuous Dynamical Systems-Series B14, (2010), 1--16 D.O.I.

S. Calogero, P. Chruściel, J. Nieto, J. Soler, La Relatividad se debate en Granada,, 05/abr/2010.

P.E. Jabin, J. Soler, A coupled Boltzmann & Navier-Stokes fragmentation model induced by a fluid-particle-spring interaction, SIAM Multiscale Model. Simul. 8(4), (2010), 1244--1268 D.O.I.


Battaner E, Soler J., Las matemáticas de la materia oscura, Las ecuaciones de la estabilidad de las galaxias o por qué el cielo no cae sobre nuestras cabezas, El Paí, 01/abr/2009.

Battaner E, Soler J., Size of a galaxy can be determined by its dark matter, physicists and mathematicians show, Science Daily, june 9, 2009.

Bellomo N., Bellouquid A., Soler J., On the Derivation of Hyperbolic Macroscopic Tissue Models. From the Mathematical Kinetic Theory for Active Particles, Mathematical and Computer Modelling 49, (2009), 2083--2093. D.O.I.

Calogero S., Sánchez O., Soler J., Asymptotic behavior and orbital stability of galactic dynamics in relativistic scalar gravity, Archive Rat. Mech. Anal. Vol. 194, (2009), 743--773. D.O.I.

Calvo J., Florido E., Sánchez O., Battaner E., Soler J., Ruiz-Granados B.,On an unified theory of cold dark matter halos based on collisionless Boltzmann-Poisson polytropes, Physica A, Statistical Mechanics and its Applications Vol. 388, (2009), 2321--2330. D.O.I.

Soler J., Expertos de la UGR predicen el desarrollo de procesos tumorales mediante las matemáticas, Andalucía Investiga, 04/feb/2009.


Bellomo N., Bellouquid A., Nieto J., Soler J., Multicellular biological growing systems: hyperbolic limits towards macroscopic description, Math. Mod. and Meth. in Appl. Sci. Vol. 17 Suppl., (2007), 1675--1692.


Bechouche, P., Poupaud, F., Soler, J., Quantum Transport and Boltzmann Operators, Journal of Statistical Physics Vol. 122, No. 3, (2006), 417--436.

Bonilla, L.L., Pérez-Vicente, C.J., Ritort, F., Soler, J., Exact solutions and dynamics of globally coupled oscillators, Math. Mod. Meth. Appl. Sci., Vol. 16(12), (2006), 1919--1959.

Bokanowski, O., López, J.L., Sánchez, O., Soler, J., Long time behaviour to the Schrödinger-Poisson-Xα systems, Mathematical Physics of Quantum Mechanics Selected and Refereed Lectures from QMath9 Series: Lecture Notes in Physics Vol 690, (2006) XXI, 485 p.

Jabin, P.E., Soler, J., A kinetic description of particle fragmentation, Math. Mod. Meth. Appl. Sci., Vol. 16(6), (2006), 933--948.

Sánchez, O., Soler, J., Orbital stability for polytropic galaxies, Annales de l'IHP- Analyse non linéaire Vol. 23(6), (2006), 781--802.


Goudon, T., Nieto, J., Soler, J., Poupaud, F., Multidimensional high-field limit of the electrostatic Vlasov-Poisson-Fokker-Planck system, J. Diff. Eq. 213, (2005), 418--442.

D. Jiroveanu, J. Soler, Numerical Modeling of a bubble breakup behavior in homogeneous and isotropic turbulence, New Trends in Continuum Mechanics, 159-168, Theta 2005.


Arnold, A., López, J.L., Markowich, P.A., Soler, J., An analysis of Wigner-Fokker-Planck models: a Wigner function approach, Rev. Mat. Iberoamericana. 20, (2004), 771--818.

Bonilla, L.L., Sánchez, O., Soler, J., Random domain-relocation times in semiconductor superlattices: a stochastic discrete drift-diffusion approach, Progress in Industrial Mathematics at ECMI 2002. Series: Mathematics in Industry. The European Consortium for Mathematics in Industry, Edited by Buikis, A., Ciegis, R., Fitt, A.D., (2004).

Dolbeault, J., Sánchez, O., Soler, J., Asymptotic behaviour for the Vlasov-Poisson system in the stellar dynamic case, Arch. Rat. Mech. Anal. 171, (2004), 301--327.

Goudon, T., Sánchez, O., Soler, J., Bonilla, L.L., Low-field limit for a nonlinear discrete drift-diffusion model arising in semiconductor superlattices theory, SIAM Journal on Applied Mathematics Vol. 64, no. 5, (2004), 1526--1549

Liñán, A., Kurdyumov, V., Soler, J., The flow field in the slender combustion chambers of solid propelant rockets, in Simplicity, Rigor and Relevance in Fluid Mechanics. A volume in honor of Amable Liñán, Editors: F.J. Higuera, J. Jiménez, J.M. Vega, CIMNE, Barcelona 2004, 127- 141.

Sánchez, O., Soler, J., Long-time dynamics of the Schödinger-Poisson-Slater system, J. Stat. Phys. Vol. 114, no. 1/2, (2004), 179--204.

Sánchez, O., Soler, J., Asymptotic decay estimates for the repulsive Schrödinger-Poisson system, Math. Methods Appl. Sci. 27, (2004), 371--380.


Bokanowski, O., López, J.L., Soler, J., On an exchange interaction model for quantum transport: the Schrödinger-Poisson-Slater system, Math. Models Methods Appl. Sci. 13(10), (2003), 1--16

Frommlet, F., López, J.L., Soler, J., Toscani, G., Nonlinear rescalings, dispersion relations and conservation laws for some linear kinetic and quantum-kinetic problems, Comm. Appl. Nonlinear Anal. 10, no. 3, (2003), 1--20.


Bechouche, P., Nieto, J., Ruiz-Arriola, E., Soler, J., On a variational approach to the time evolution of the mean field polaron, pp. 358--364. Progress in Industrial Mathematics at ECMI 2000, Mathematics in Industry, VOL. 1, Springer (2002).

Bonilla, L.L., Sánchez, O.,Soler, J., Nonlinear stochastic discrete drift-diffusion theory of charge fluctuations and domain relocation times in semiconductor superlattices, Physical Review B65, (2002), 195308.

López, J.L., Soler, J., Toscani, G., Time rescaling and asymptotic behavior of some fourth order degenerate diffusion equations, Comput. Math. Appl. 43, No. 6-7, (2002), 721--736.

Nieto, J., Poupaud, F., Soler, J., About uniqueness of weak solutions to first order quasi-linear equations, Math. Mod. Methods in Appl. Sci. 12, No.11, (2002), 1599-1605.

Ruiz-Arriola, E., Soler, J., Quantum Kinetic Equation including phonon scattering, pp. 347--357. Progress in Industrial Mathematics at ECMI 2000, Mathematics in Industry, VOL. 1, Springer (2002).


Bechouche, P., López, J.L., Soler, J., Long-time asymptotics for semiconductor crystals, Nonlinear Analysis TMA., Vol. 47, No. 9, (2001), 5861--5872.

Bonilla, L.L., Soler, J., High-field limit of the Vlasov-Fokker-Planck system. A comparison of different perturbations methods, Math. Mod. Methods Appl. Sci. Vol. 11, No. 8, (2001), 1457--1468.

Nieto, J., Poupaud, F., Soler, J., High field limit for the Vlasov-Poisson-Fokker-Planck system, Arch. Rational Mech. Anal. 158, no. 1, (2001), 29--59.

Ruiz-Arriola, E., Soler, J., A variational approach to the Schrödinger-Poisson system: asymptotic behaviour, breathers and stability, J. Stat. Phys., Vol. 103, nos. 5/6, (2001), 1069--1105.


Bechouche, P., Nieto, J., Ruiz-Arriola, E., Soler, J., On the time evolution of the mean-field polaron. J. Math. Phys., Vol 41, No. 7, (2000), 4293--4312.

Carrillo, J.A., Soler, J., On the evolution of an angle in a vortex patch, J. Nonlinear Sci. Vol. 10, (2000), 23--47..

López, J.L., Soler, J., Asymptotic behaviour to the 3-D Schrödinger/Hartree-Poisson and Wigner-Poisson systems, Math. Mod. Methods in App. Sci., Vol. 10, No. 6, (2000), 923--943.

Poupaud, F., Soler, J., Parabolic limit and stability of the Vlasov-Poisson-Fokker-Planck system, Math. Mod. Methods in App. Sci., Vol. 10, No 7, (2000), 1027--1045.

Ringhofer, C., Soler, J., Discrete Schrödinger-Poisson systems preserving energy and mass, Applied Mathematics Letters 13, (2000), 27--32.


Carrillo, J.A., Soler, J., On the evolution of a singular vortex patch in a two-dimensional incompressible fluid flow, Computer Physics Communications121-122, (1999), 244--250.

Ruiz-Arriola, E., Soler, J., Asymptotic behaviour for the 3-D Schrödinger-Poisson system in the attractive case with positive energy, Applied Mathematics Letters12, (1999), 1--6.


Bonilla, L.L., Perez-Vicente, C.J., Ritort, F., Soler, J., Exactly solvable phase oscillators models with synchronization dynamics, Phys. Rev. Lett. 81, (1998), 3643--3646.

Carrillo, J.A., Soler, J., On functional solutions for the three dimensional kinetic equations of Vlasov-type with bounded measures as initial data, Nonlinear Analysis 32, (1998), 235--259.


Bonilla, L.L., Carrillo, J.A., Soler, J., Asymptotic behaviour of the initial boundary value problem for the Vlasov-Poisson-Fokker-Planck system, SIAM J. Appl. Math. 57, (1997), 1343--1372.

Carrillo, J.A., Soler, J., Functional solutions for the Vlasov-Poisson system, Appl. Math. Lett. 10, (1997), 45--50.

Carrillo, J.A., Soler, J., On the Vlasov-Poisson-Fokker-Planck equations with measures in Morrey spaces as initial data, J. Math. Anal. Appl. 207, (1997), 475--495.

López, J.L., Soler, J., Scaling limits for the 3-D Schrödinger-Poisson systems, Appl. Math. Letters 10, (1997), 61--65.

Soler, J., Asymptotic behaviour for the Vlasov-Poisson-Fokker-Planck system. Nonlinear Analysis, TMA 30, (1997), 5217--5228.


Bonilla, L.L., Carrillo, J.A., Soler, J., An H-theorem for electrostatic and self-gravitating Vlasov-Poisson-Fokker-Planck systems, Physics Letters A 212, (1996), 55--59.

Bonilla, L.L., Carrillo, J.A., Soler, J., Asymptotic behavior of the Vlasov-Poisson-Fokker-Planck system in bounded domains, Z. Angew. Math. Mech. 76, (1996), 485--486.

Carrillo, J.A., Soler, J., Vázquez, J.L., Asymptotic behaviour and selfsimilarity for the three dimensional Vlasov-Poisson-Fokker-Planck system, J. Functional Analysis 141, (1996), 99--132.

Soler, J., On weak solutions of the Vlasov-Poisson-Fokker-Planck equations, Vestn. Mosk. U. Math. Mech. 6, (1996), 19--20.

Soler, J., On uniqueness of solutions for the 2-D Euler equations, Z. Angew. Math. Mech. 76, (1996), 105--109.