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

Brief CV

Teaching

• MATH44041/64041: Applied Dynamical Systems (also on blackbloard)
• MATH19872 0D2

Past Teaching

Undergraduate/Applied MSc Projects

Research

• 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

• 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

• 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)

• 17-19 September 2018, Recent Developments in the Study of Growth Processes, Warwick
• 24-26 April 2019, British Applied Mathematics Colloquium, Bath
• 15-19 July 2019, International Congress on Industrial and Applied Mathematics (ICIAM) , VAlencia, Spain
• 16-20 September 2019, Dynamics, Equations and Applications (DEA 2019)