PUBLICATIONS

Working papers:

[i] R. J. Alonso, P. Gervais & B. Lods, Conditional integrability and stability for the homogeneous Boltzmann equation with very soft potentials,  submitted for publication, 2024.

[ii] R. J. Alonso, V. Bagland, J. A. Canizo, B. Lods & S. Throm, Relaxation in Sobolev spaces and L^1 spectral gap of the 1D dissipative Boltzmann equation with Maxwell interactions, submitted for publication, 2024.

[iii] R. J. Alonso, V. Bagland, J. A. Canizo, B. Lods & S. Throm, One-dimensional inelastic Boltzmann equation: Stability and uniqueness of self-similar L^1-profiles for moderately hard potentials, submitted for publication, 2024.

[iv] B. Lods  & M. Mokhtar-Kharroubi, A new quantitative tauberian approach to long-time asymptotics of perturbed stochastic semigroups, in preparation.

[v] R. J. Alonso, V. Bagland, J. A. Canizo, B. Lods & S. Throm, One dimensional inelastic Boltzmann equation: regularity and uniqueness of self-similar profiles for moderately hard potentials, submitted for publication, 2022. This manuscript will not be published. The main results contained here have been improved in the two papers [ii] and [iii] but several material of independent interest can be found only  in [v] which remains available online.

[vi] B.  Lods  & M. Mokhtar-Kharroubi, Quantitative tauberian approach to collisionless transport equations with diffuse boundary operators, 2020. This manuscript will not be published. The main results contained here have been extended and improved in the paper [56] but several material of independent interest can be found only  in [vi] which remains available online. 

Publications in refereed journals:

[62] T. Borsoni & B. Lods, Quantitative relaxation towards equilibrium for solutions to the Boltzmann-Fermi-Dirac equation with cutoff hard potentials,  Journal of Functional Analysis, Vol. 287, article 110599 (48p.), 2024.

[61] P. Gervais, B. Lods, Hydrodynamic limits for kinetic equations preserving mass, momentum and energy: a spectral and unified approach in the presence of a spectral gap, Annales Henri Lebesgue, Vol. 7, pp. 969-1098, 2024.

[60] R. J. Alonso, V. Bagland, L. Desvillettes, B. Lods,  A priori estimates for solutions to Landau equation under Prodi-Serrin's like criteria, Archive for Rational Mechanics and Analysis, Vol. 248, article 42 (63p.), 2024.

[59] R. J. Alonso, V. Bagland, & B. Lods, The Landau equation with moderate soft potentials: an approach using ϵ-Poincaré inequality and Lorentz spaces, Journal of Differential Equations,Vol. 395, pp. 69-105, 2024.

[58] R. J. Alonso, B. Lods & I. Tristani, Fluid dynamic limit of Boltzmann equation for granular hard spheres in a nearly elastic regime, Mémoires de la Société Mathématique de France, accepted for publication, 2024.

[57]  B. Lods  & M. Mokhtar-Kharroubi, Convergence rate to equilibrium for conservative scattering models on the torus: A new tauberian approach,  Transactions of the American Mathematical Society,  Vol. 377, 2741-2820, 2024.

[56] B. Lods, M. Mokhtar-Kharroubi, Convergence rate to equilibrium for collisionless transport equations with diffuse boundary operators: A new tauberian approach,  Journal of Functional Analysis,  Vol. 283, article 109671 (100p.), 2022.

[55] R. J. Alonso, V. Bagland, L. Desvillettes, B. Lods, About the Landau-Fermi-Dirac equation with moderately soft potentials, Archive for Rational Mechanics and Analysis, Vol. 244, 779-875, 2022.

[54] R. J. Alonso, B. Lods & I. Tristani, From Boltzmann equation for granular gases to a modified Navier-Stokes-Fourier system, Journal of Statistical Physics,  Vol. 187, article 28 (31p.), 2022.

[53] B. Lods  & M. Mokhtar-Kharroubi, On eventual compactness of collisionless kinetic semigroups with velocities bounded away from zero, Journal of Evolution Equations,  Vol. 22, article 25 (36 p.), 2022.

[52] R. J. Alonso, V. Bagland, L. Desvillettes, B. Lods, About the use of entropy production for the Landau-Fermi-Dirac equation,  Journal of Statistical Physics, Vol. 183, article 10 (27 p.), 2021.

[51] R. J. Alonso, V. Bagland, B. Lods, Long time dynamics for the Landau-Fermi-Dirac equation with hard potentials, Journal of Differential Equations, Vol. 270, 596-663, 2021.                         

[50] J. A. Canizo, B. Lods & S. Throm, Contractivity for Smoluchowski's coagulation equation with solvable kernels, Bulletin of the London Mathematical Society, Vol. 53, 248-258, 2021.

[49] A. Nota, B. Lods & F. Pezzotti, A Kac model for kinetic annihilation, Journal of Nonlinear Science,  Vol. 30, 1455–1501, 2020.

[48] B. Lods, M. Mokhtar-Kharroubi, R. Rudniki, Invariant density and time asymptotics for collisionless kinetic equations with partly diffuse boundary operators, Annales de l'Institut Henri Poincaré C, Analyse Non Linéaire, Vol. 37, 877-923, 2020.

[47]  R. J. Alonso, V. Bagland & B. Lods, Convergence to self-similarity for ballistic annihilation dynamics, Journal de Mathématiques Pures et Appliquées, Vol. 138, 88-163, 2020.

[46] A. Nota, R. Winter & B. Lods, Kinetic description of a Rayleigh Gas with annihilation,  Journal of Statistical Physics,  Vol 176, 1434–1462, 2019.

[45] R. J. Alonso, V. Bagland & B. Lods, Uniform estimates on the Fisher information for solutions to Boltzmann and Landau equations, Kinetic and Related Models, Vol 12, 1163-1183, 2019.

[44] L. Arlotti & B. Lods, An Lp-approach to the well-posedness of transport equations associated to a regular field - Part II, Mediterranean Journal of Mathematics, Vol 16: 152, 2019.

[43] L. Arlotti & B. Lods, An Lp-approach to the well-posedness of transport equations associated to a regular field - Part I, Mediterranean Journal of Mathematics, Vol 16: 145, 2019.

[42] J. A. Canizo, A. Einav & B. Lods, Uniform propagation of moments for the Becker-Doring equation, Proceedings of the Royal Society of Edinburgh, section A,  Vol 149, 995–1015, 2019. 

[41] R. J. Alonso, V. Bagland, Y. Cheng & B. Lods, One dimensional dissipative Boltzmann equation: measure solutions, cooling rate and self-similar profile, SIAM Journal of Mathematical Analysis, Vol. 50, 1278-1321, 2018.

[40] J. A. Canizo, A. Einav & B. Lods, On the Rate of Convergence to Equilibrium for the Linear Boltzmann Equation with Soft Potentials, Journal of Mathematical Analysis and Applications, Vol. 462, 801-839, 2018.

[39] J. A. Canizo, A. Einav & B. Lods, Trend to equilibrium for the Becker-Döring equations: an analogue of Cercignani's conjecture, Analysis and PDE, Vol. 10, 1663-1708, 2017.  

[38] B. Lods  & M. Mokhtar-Kharroubi, Convergence to equilibrium for linear spatially homogeneous Boltzmann equation with hard and soft potentials: a semigroup approach in L^1 spaces, Mathematical Methods in Applied Sciences, Vol. 40, 6527-6555, 2017.

[37] J. A. Canizo & B. Lods, Exponential trend to equilibrium for the inelastic Boltzmann equation driven by a particle bath, Nonlinearity, Vol. 29, 1687-1716, 2016.

[36] V. Bagland & B. Lods, Uniqueness of the self-similar profile for a kinetic annihilation equation, Journal of Differential    Equations, Vol. 259, 7012-7059, 2015.

[35] B. Lods & G. Pistone, Information geometry formalism for the spatially homogeneous Boltzmann equation, Entropy, Vol. 17, 4223-4263, 2015.

[34] M. Bisi, J. A. Canizo & B. Lods, Entropy dissipation estimates for the linear Boltzmann operator, Journal of Functional Analysis, Vol. 269, 1028-1069, 2015.

[33] R. J. Alonso & B. Lods, Boltzmann model for viscoelastic particles: asymptotic behavior, pointwise lower bounds and regularity, Communications in Mathematical Physics, Vol. 331, 545-591, 2014.

[32] L. Arlotti & B. Lods, Transport semigroup associated to positive boundary conditions of unit norm: a Dyson-Phillips approach, Discrete and Continuous Dynamical Systems, Series B,  Vol. 19, 2739-2766, 2014. 

[31] L. Arlotti, B. Lods  & M. Mokhtar-Kharroubi, Non autonomous honesty theory for positive evolution families in abstract   state spaces with applications to linear kinetic equations, Communications on Pure and Applied Analysis, Vol. 13, 729-771, 2014.

[30] J. A. Canizo & B. Lods, Exponential convergence to equilibrium for subcritical solutions of the Becker-Döring equations, Journal of Differential Equations, Vol. 255, 905-950, 2013.                         

[29] R. J. Alonso & B. Lods, Uniqueness and regularity of steady states of the Boltzmann equation for viscoelastic hard-spheres  driven by a thermal bath, Communications in Mathematical Sciences, Vol. 11, 851-906, 2013.  

[28] V. Bagland & B. Lods, Existence of self-similar profile for a kinetic annihilation model, Journal of Differential Equations, Vol. 254, 3023-3080, 2013 (see also some expanded and corrected version here).

[27] R. J. Alonso  & B. Lods,Two proofs of Haff's law for dissipative gases: the use of entropy and the weakly inelastic regime, Journal of Mathematical Analysis and Applications, Vol. 397, 260-275, 2013. 

[26] M. Bisi, J. A. Canizo & B. Lods, Uniqueness in the weakly inelastic regime of the equilibrium state to the Boltzmann equation drivenby a particle  bath, SIAM Journal of Mathematical Analysis, Vol. 43, 2640-2674, 2011.

[25] L. Arlotti, B. Lods  & M. Mokhtar-Kharroubi, On perturbed substochastic semigroups in abstract state spaces, Zeitschrift für Analysis und ihre Anwendungen, Vol. 30, 457-495, 2011.

[24] L. Arlotti, J. Banasiak  B. Lods, On general transport equations with abstract boundary conditions. The case of divergence free force field,  Mediterranean Journal of Mathematics, Vol. 8, 1-35, 2011.

[23] R. J. Alonso & B. Lods, Free cooling and high-energy tails of granular gases with variable restitution coefficient,  SIAM Journal of Mathematical Analysis,  Vol. 42, No. 6, pp. 2499-2538, 2010.

[22] B. Lods, Variational characterizations of the effective multiplication factor of a nuclear reactor core Kinetic and Related Models, Vol. 2, 307-331, 2009.

[21] L. Arlotti, J. Banasiak & B. Lods, A new approach to transport equations associated to a regular field: trace results and well-posedness, Mediterranean Journal of Mathematics, Vol. 6, 367-402, 2009.

[20] B. Lods, M. Mokhtar-Kharroubi & M. Sbihi, Spectral properties of general advection operators and weighted translation semigroups, Communications on Pure and Applied Analysis, Vol. 8, 1469-1492, 2009.

[19] K. Latrach & B. Lods, Spectral analysis of transport equations with bounce-back boundary conditions, Mathematical Method in Applied Sciences, Vol. 32, 1325-1344, 2009.

[18] M. Bisi, J. A. Carrillo & B. Lods, Equilibrium solution to the inelastic Boltzmann equation driven by a particle bath, Journal of Statistical Physics, Vol. 133, 841-870, 2008. 

[17] B. Lods, C. Mouhot & G. Toscani, Relaxation rate, diffusion approximation and Fick's law for inelastic scattering Boltzmann models,   Kinetic and Related Models, Vol. 1,  223-248, 2008.

[16] K. Latrach, B. Lods & M. Mokhtar-Kharroubi, Weak spectral mapping theorems for C_0-groups associated to transport equations in slab geometry, Journal of Mathematical Analysis and Applications, Vol. 342, 1038-1051, 2008.

[15] E. De Angelis & B. Lods, On the kinetic theory for active particles:a model for tumor-immune system competition,  Mathematical and Computer Modelling, Vol. 47,  196-209, 2008.

[14] B. Lods,On the spectrum of mono-energetic absorption operator with Maxwell boundary conditions. A unified treatment, Transport theory and Statistical Physics, Vol. 37, 1-37, 2008.

[13] L. Arlotti  & B. Lods, Integral representation of the linear Boltzmann operator for granular gas dynamics with applications, Journal of Statistical Physics, Vol. 129, 517-536, 2007.

[12] L. Arlotti, J. Banasiak & B. Lods, On transport equations driven by a non divergence-free force field, Mathematical Method in Applied Sciences, Vol. 30, 2155-2177, 2007. 

[11] B. Lods & M. Sbihi, Stability of the essential spectrum for 2D-transport models with Maxwell boundary conditions, Mathematical Method in Applied Sciences, Vol. 29, 499-523, 2006. 

[10] B. Lods, On the linear Boltzmann equation for dissipative hard spheres, "Modelling and Numerics of Kinetic Dissipative Systems", Proceedings of the International Workshop "Modelling and numerics of kinetic dissipative systems: cooling, clustering, and pattern formation"; Editors L. Pareschi, G. Russo, G. Toscani, Nova Science, New York, 2006.

[9] C. Cattani, A. Ciancio & B. Lods, On a mathematical model of  immune  competition, Applied Mathematics Letters, Vol. 19, 678-683, 2006.

[8] L. Arlotti & B. Lods, Substochastic semigroups for transport equations with conservative boundary conditions, Journal of Evolution Equations, Vol. 5, 485-508, 2005.

[7] B. Lods, Semigroup generation properties of streaming operators with non-contractive boundary conditions, Mathematical and Computer Modelling, Vol. 42, 1141-1162, 2005.

[6] B. Lods & G. Toscani, Long time behavior of non-autonomous Fokker-Planck equations and the cooling of granular gase, Ukrainian Mathematical Journal, Vol. 57, 778-789, 2005.

[5] B. Lods & G. Toscani, The linear dissipative Boltzmann equation for hard spheres, Journal of Statistical Physics,  Vol. 117, 635-664, 2004.

[4] B. Lods, On linear kinetic equations involving unbounded cross-sections,  Mathematical Method in Applied Sciences,  Vol. 27, 1049-1075, 2004. 

[3] B. Lods  & M. Mokhtar-Kharroubi, On the theory of a growing cell population with zero minimum cycle length, Journal of Mathematical Analysis and Applications, Vol. 266, 70-99, 2002.

[2] B. Lods, A generation theorem for kinetic equations with non-contractive boundary operators, Comptes Rendus de l’Académie des Sciences, Paris, Paris, Vol. 335, Série I, 655-660, 2002.

[1] K. Latrach & B. Lods, Regularity and time asymptotic behaviour of solutions to transport equations, Transport theory and Statistical Physics, Vol. 30, no 7, 617-639, 2001.

Book:

[] N. Bellomo, B. Lods, R. Revelli & L. Ridolfi, Generalized collocation methods for nonlinear problems in applied sciences, Birkhauser, Modelling and simulation in engineering and technology, Boston, 2008.