Department of Applied Mathematics

Applied Analysis

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Applied Mathematics
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Applied Analysis

The applied analysis research group studies mathematical problems arising from physical, chemical, geophysical, biophysical, and materials sciences. These problems often are described by time-dependent partial, ordinary, or integral differential equations, together with sophisticated boundary conditions, interface conditions, and external forcing. Nonlinear dynamical systems offer a geometrical and topological framework for detecting, understanding, and quantifying complex phenomena of these time-dependent differential equations. Partial differential equation theory allows us to correctly formulate well-posed problems and to examine behaviors of solutions, setting the stage for efficient numerical simulations. Nonlocal equations arise from macroscopic modeling of stochastic dynamical systems with Lévy noise and from modeling long-range interactions, and consequently give an understanding of anomalous diffusions.

Faculty with a Primary or Secondary Interest in Applied Analysis

Sergey Nadtochiy

Professor of Applied Mathematics

Jinqiao (Jeffrey) Duan

Professor Emeritus of Applied Mathematics

Arthur Lubin

Associate Professor of Applied Mathematics

Related Seminars

Recent Research Grants

NSF DMS- 2309798 (PI S. Li), Collaborative Research: : Mathematical modeling and computation of morphological instabilities in reactive fluids driven out of equilibrium. Start date: 07/01/2023; End date: 06/30/26. $242,677. Shuwang’s Role: PI.
NSF DMS- 2244553, REU Site: Summer Undergraduate Research Experience (SURE) at Illinois Tech. Start date: 05/01/2023; End date: 04/30/2026. $404,893. Shuwang’s Role: Senior personnel (PI: Yuhan Ding).
NSF DMS-2205751 (PI S. Nadtochiy), 2022–2025.NSF CAREER Grant DMS-1855309 (PI S. Nadtochiy), 2017–2022.
NSF DMS-1620449 (PI X. Li and Co-PI J. Duan): Theoretical and Numerical Studies of Nonlocal Equations Derived from Stochastic Differential Equations with Lévy Noises, 2016-2020.
NSF DMS-1642545 (PI J. Duan and Co-PI X. Li): CBMS Conference: Nonlocal Dynamics — Theory, Computation and Applications, 2017-2018.

Recent Publications

Dong, H., Zhao, Z., Li, S. et al. Second Order Convergence of a Modified MAC Scheme for Stokes Interface Problems. J Sci Comput 96, 27 (2023). https://doi.org/10.1007/s10915-023-02239-w
Tang, X., Li, S., Lowengrub, J.S. et al. Phase field modeling and computation of vesicle growth or shrinkage. J. Math. Biol. 86, 97 (2023). https://doi.org/10.1007/s00285-023-01928-2
A. Barua, R. Chew, S. Li, et al. Sharp-interface problem of the Ohta-Kawasaki model for symmetric diblock copolymers, Journal of Computational Physics 481, 112032, (2023).https://doi.org/10.1016/j.jcp.2023.112032
Z. Jin, Y. Cao, S. Li, W. Ying and M. Krishnamurthy. A Kernel-Free Boundary Integral Method for 2-D Magnetostatics Analysis. IEEE Transactions on Magnetics, vol. 59, no. 4, pp. 1-19, April 2023, Art no. 7400319, doi: 10.1109/TMAG.2023.3247444
H Feng, A Barua, S Li, X Li. Boundary integral simulations of boundary layers in linear viscoelastic flow. Physics of Fluids 35, 023108 ( 2023). https://doi.org/10.1063/5.0138344
Lu, MJ., Hao, W., Hu, B. et al. Bifurcation analysis of a free boundary model of vascular tumor growth with a necrotic core and chemotaxis. J. Math. Biol. 86, 19 (2023). https://doi.org/10.1007/s00285-022-01862-9
G. Alonso Alvarez, S. Nadtochiy, and K. Webster “Optimal brokerage contracts in Almgren-Chriss model.” To appear in SIAM Journal on Financial Mathematics
S. Nadtochiy and M. Shkolnikov “Stefan problem with surface tension: global existence of physical solutions under radial symmetry.” Probability Theory and Related Fields, published online, 2023
S. Nadtochiy, M. Shkolnikov, and X. Zhang “Scaling limits of external multi-particle DLA on the plane and the supercooled Stefan problem.” To appear in Annales de l’Institut Henri Poincare
J.-F. Chassagneux, S. Nadtochiy, and A. Richou “Reflected BSDEs in non-convex domains.”Probability Theory and Related Fields, 183:1237-1284, 2022
S. Nadtochiy “A simple microstructural explanation of the concavity of price impact. Mathematical Finance, 32(1):78-113, 2022
I. Ekren and S. Nadtochiy “Utility-based hedging and indifference price of contingent claims in Almgren-Chriss model with temporary impact.” Mathematical Finance, 32(1):172-225, 2022
F. Delarue, S. Nadtochiy and M. Shkolnikov “Global Solution to Super-cooled Stefan Problem with Blow-ups: Regularity and Uniqueness.” Probability and Mathematical Physics, 3(1):171-213, 2022
S. Nadtochiy and M. Shkolnikov “Mean Field Systems on Networks, with Singular Interaction through Hitting Times.” Annals of Probability, 48(3):1520–1556, 2020
R. Gayduk and S. Nadtochiy “Control-Stopping Games for Market Microstructure and Beyond.” Mathematics of Operations Research, 45:1289–1317, 2020