Yanghong Huang
Lecturer in Applied Mathematics
School of Mathematics,
University of Manchester
Office: Alan Turing Building 1.108
Phone: 0161-3063657
Email:
Office Hour: Thursday 11:00-12:00
Teaching
Research
General Research Interest:
- Applied analysis for differential and integral equations from mathematical biology and collective behaviours of particle systems, asymptotic analysis of
steady states and solutions close to blowup
- Numerical methods for gradient flow system and equations with nonlocal interactions (including fractional Laplacians)
- Pattern formation of reaction-diffusion equations
Current Research Projects:
- Finite difference discretisation of fractional Laplacian
- Discontinuous Galerkin Method for gradient flow type equations
- Particle approximation of gradient flow systems
- Exact and asymptotic stable steady solutions of non-local
interaction models, like the aggregation with power-law potentials
Publications
-
D. Greco, Y. Huang, Z. Liu and V. Moroz. On a class of Thomas-Fermi type
variational problems, preprint, 2024
-
S. Keshav, S. Singh, Y. Huang, M. Singh and Jitendra Kumar.
An coupled meshfree approach and its convergence for fragmentation equation
in the presence of source and efflux terms: Longer dynamical behaviour, 2023
- Y. Huang, E. Mainini, J. L. Vazquez and B Volzone.
Nonlinear aggregation-diffusion equations with Riesz potentials
, Journal of Functional Analysis, 287(2), 2024
-
H. Chan, M.D.M. Gonzalez, Y. Huang, E. Mainini, and B. Volzone,
. Uniqueness of entire ground states for the fractional
plasma problem. Calculus of Variations and Partial Differential Equations,
59, Article number: 195, 2020
- F. Feo, Y. Huang and B. Volzone, Long-time asymptotics for nonlocal porous medium equation with absorption or convection.
Communications in Contemporary Mathematics,
22(03):1950015,
Journal,
2020
- X. Wang, W. Shang, X. Li, J. Duan and Y. Huang,
Fokker-Planck equation driven by asymmetric Levy motion.
Advances in Computational Mathematics, 45(2), pp. 787--811, 2019.
Journal,
Preprint.
- Y. Huang and A. Oberman. Finite Difference Methods for Fractional Laplacians.
Preprint
- J.A. Carrillo, Y. Huang and M. Schmidtchen,
Zoology of a non-local cross-diffusion model for two species,
SIAM J. Appl. Math., 78(2), pp. 1078-1104, 2018.
Journal,
Preprint.
- Y.Huang and X. Wang,. Finite Difference Methods for the generator of 1D asymmetric alpha-stable
Levy motions. Comput. Methods Appl. Math., 18(1), pp. 63--76, 2018.
journal,
preprint.
- J.A. Carrillo, Y. Huang, F. S. Patacchini and G. Wolansky. Numerical Study of a Particle Method for Gradient Flows.
Kinetic and Related Models, 10(3), pp. 613 - 641, 2017.
journal,
preprint.
- J.A. Carrillo, Y. Huang. Explicit Equilibrium Solutions For the Aggregation Equation with Power-Law Potentials. Kinetic and Related Models, 10(1), pp. 171 - 192, 2017.
journal,
preprint.
- J.A. Carrillo, A. Chertock, Y. Huang. A Finite-Volume Method for
Nonlinear Nonlocal Equations with a Gradient Flow Structure.
Commun. Comput. Phys., 17 (1), pp. 233-258, 2015,
journal,
preprint.
- J. A. Carrillo, Y. Huang, M. C. Santos and J. L. Vazquez.
Exponential Convergence Towards Stationary States for the 1D Porous
Medium Equation with Fractional Pressure. J. Differential.
Equations., 258(3):736-763, 2015.
journal,
preprint
- Y. Huang, A. Oberman. Numerical Methods for the Fractional Laplacian: a Finite Difference-quadrature Approach.
SIAM J. Numer. Anal., 52(6), 3056-3084., 2014.
journal,
preprint.
- J.A. Carrillo, M. Chipot, Y. Huang. On global minimizers of
repulsive-attractive power-law interaction energies.
Phil. Trans. R. Soc. A., 372:20130399, 2014.
journal,
preprint.
- Y. Huang. Explicit Barenblatt Profiles for Fractional Porous Medium
Equations,
Bull. London Math. Soc. ,46 (4): 857-869, 2014.
journal,
preprint.
- J.A. Carrillo, Y. Huang, S. Martin. Explicit Flock Solutions for
Quasi-Morse potentials, European J. Appl. Math.
, 25(5): 553-578, 2014.
journal,
preprint.
- M. Burger, R. Fetecau, Y. Huang, Stationary States and Asymptotic Behaviour of Aggregation Models with Nonlinear Local Repulsion,
SIAM J. Appl. Dyn. Syst., 13(1):397-424, 2014.
journal,
preprint,
Supplementary movies
- J.A. Carrillo, Y. Huang, S. Martin. Nonlinear stability of flock solutions in second-order swarming models,
Nonlinear Analysis: Real World Applications,17(0):332-343, 2014.
journal,
preprint.
- T. Kolokolnikov, Y. Huang and M. Pavlovski,
Singular patterns for an aggregation model with a confining potential.
Physica D, 260:65-76, 2013.
journal,
preprint.
- R. Fetecau and Y. Huang, Equilibria of biological aggregations with nonlocal repulsive-attractive interactions.
Physica D, 260:49-64, 2013.
journal,
preprint.
- Y. Huang, T.P Witelski, A.L. Bertozzi.
Anomalous exponents of self-similar solutions to an aggregation equation in odd dimensions.
Appl. Math. Lett.,25(12):2317-2321, 2012.
journal,
preprint.
- Y. Huang, A.L. Bertozzi. Asymptotics of Blowup Solutions for the Aggregation Equation.
Discrete Contin. Dyn. Syst. Ser. B, 17(4):1309-1331, 2012.
journal,
preprint.
- R. Fetecau, Y. Huang, and T. Kolokolnikov.Swarm dynamics and equilibria for a nonlocal aggregation model.
Nonlinearity, 24(10):2681, 2011.
journal,
preprint.
- Yanghong Huang, Andrea Bertozzi.
Self-similar blowup solutions to an aggregation equation.
SIAM J. Appl. Math., 70(7):2582-2603, 2010.
journal,
preprint
- Andris M. Dimits , Chiaming Wang , Russel Caflisch , Bruce I. Cohen, Yanghong Huang.
Understanding the accuracy of Nanbu's numerical Coulomb collision operator,
J. Comput. Phys.,228(13):4881-4892, 2009.
journal.
- Zhijun Tan, Yanghong Huang, An alternating Crank-Nicolson method for the numerical solution of the phase-field equations using adaptive
moving meshes,
Internat. J. Numer. Methods Fluids, 56(9):1673-1693, 2008.
journal,
preprint.
- Yanghong Huang,
Optimal Design for the Grating Coupler of Surface Plamons.
Proceedings of the COMSOL Users Conference 2008, Boston
Upcoming Conferences and Workshops (Past Events)