Papers ordered by topic (or by year)
Mathematical biology
Ecology

[68] D. Hilhorst, T.N. Nguen, YJK, and H. Park, Hyperbolic limit for a biological invasion, DCDS-B (2023) (preprint, DOI)
[65] Hao Wang, Kai Wang, and YJK, Spatial segregation in reaction-diffusion epidemic models, SIAM Appl. Math. 82 (2022) 1680--1709 (preprint, DOI)
[64] Matthieu Alfaro, Thomas Giletti, YJK, Gwenael Peltier, and Hyowon Seo, On the modelling of spatially heterogeneous nonlocal diffusion: deciding factors and preferential position of individuals, J. Math. Biol. 84 (2022) 38, (preprint, DOI)
[62] E. Brocchieri, L. Corrias, H. Dietert, and YJK, Evolution of dietary diversity and a starvation driven cross-diffusion system as its singular limit, (2021) 83, (40 pages) (preprint, DOI)
[56] YJK, Hyowon Seo, and Changwook Yoon, Asymmetric dispersal and evolutional selection in two-patch system, Discrete Continuous Dynamical Systems (2019), 40(6): 3571--3593. (preprint, DOI)
[53] Jieun Choi and YJK, Predator-prey equations with constant harvesting and planting, Journal of Theoretical Biology 458 (2018), 47-57, (preprint, DOI)
[48] J. Chung, YJK, O. Kwon, X. Pan, Discontinuous nonlinearity and finite time extinction, SIMA (2020), (preprint, DOI)
[45] Danielle Hilhorst, YJK, Dohyun Kwon, Thanh Nam Nguyen, Dispersal toward food: a study of a singular limit of an Allen-Cahn equation, J. Math. Biol. 76 (2018), 531-565. (preprint, DOI)
[36] J. Chung, YJK, O. Kwon and C. Yoon, Parameter regimes for biological advection and cross-diffusion, Mathematics in Science and Industry (2018), (preprint)
[35] YJK and O. Kwon, Evolution of dispersal with starvation measure and coexistence, Bull. Math. Biol. 78 (2016), 254-279 (preprint, DOI)
[25] YJK,O. Kwon and F. Li, Evolution of dispersal toward fitness, Bull. Math. Biol. 75(12) (2013) 2474--2498 (preprint, DOI)
[24] YJK, O. Kwon and F. Li, Global asymptotic stability and the ideal free distribution in a starvation driven diffusion, J. Math. Biol. 68(6) (2014) 1341-1370 (preprint, DOI)
[23] E.Cho and YJK, Starvation driven diffusion as a survival strategy of biological organisms, Bull. Math. Biol. 75(5) (2013) 845--870 (preprint, DOI)

Chemotaxis

[70] YJK, Masayasu Mimura, and C. Yoon, Nonlinear diffusion for bacterial traveling wave phenomenon, Bull. Math. Biol. 85 (2023), 35 (preprint, DOI)
[54] L. Desvillettes, YJK, A. Trescases, and C. Yoon, A logarithmic chemotaxis model featuring global existence and aggregation. Nonlinear Anal. Real World Appl. 50 (2019), 562-582. (preprint, DOI)
[52] Beomjun Choi and YJK, Diffusion of biological organisms; Fickian and Fokker-Planck type diffusions (2018), submitted to SIAP (preprint, DOI)
[50] Hai-Yang Jin, YJK, Zhi-An Wang, Global dynamics and pattern formation under density-suppressed motility, SIAM J. Appl. Math. 78 (2018), no. 3, 1632-1657. (DOI)
[44] S. Choi and YJK, A discrete velocity kinetic model with food metric: chemotaxis traveling waves, Bull. Math. Biol. (2017), (preprint, DOI)
[42] Changwook Yoon and YJK, Global existence with pattern formation in cell aggregation model, Acta. Appl. Math. (2017) (preprint, DOI)
[34] S. Choi and YJK, Chemotactic traveling waves by the metric of food, SIAM J. Appl. Math. 75 (2015) no.5 2268-2289, (preprint, DOI)
[27] C. Yoon and YJK, Bacterial chemotaxis without gradient-sensing, J. Math. Biol. 70 (2015), no.6, 1359-1380 (preprint, DOI)

Traveling waves

[67] YJK and C. Yoon, Modeling bacterial traveling wave patterns with exact cross-diffusion and population growth, DCDS-B (2023) (preprint, DOI)
[66] Thomas Giletti, Ho-Youn Kim, and YJK, Terrace solutions for non-Lipschitz multistable nonlinearities, SIAM Math. Anal. 54 (2022) 4785--4805 (preprint, DOI) [55] Sunho Choi and YJK, Chemotactic traveling waves with compact support, J. Math. Aanl. Appl., (2020) 488(2), 124090 (preprint, DOI)
[46] S. Choi, J Chung, YJK, Inviscid traveling waves of monostable nonlinearity, submitted to Appl. Math. Lett. (2017), (preprint, DOI)
[40] Danielle Hilhorst and YJK, Diffusive and inviscid traveling waves of the Fisher equation and nonuniqueness of wave speed, Appl. Math. Lett. 60 (2016) 28-35 (preprint, DOI)
[38] J. Chung and YJK, Bistable nonlinearity with a discontinuity and traveling waves with a free boundary, submitted to DCDS (preprint)
[26] YJK, W.-M. Ni and M. Taniguchi, Non-existence of localized travelling waves with non-zero speed in single reaction-diffusion equations, Discrete Contin. Dyn. Syst. 33 (2013), no. 8, 3707-3718. (preprint, DOI)

Non-uniform Brownian motion and random walk

[33] J. Chung, YJK, and M. Lee, Random walk with heterogeneous sojourn times, submitted to Math annalen (preprint, DOI)
[31] YJK, Einstein's random walk and thermal diffusion, (preprint)

Inverse problem

[43] M.-S. Ko and YJK, Resistivity tensor imaging via network discretization of Faraday's law, SIAM J. Imaging Sci. 10 (2017), 1-25 (preprint, DOI)
[39] M.G. Lee and YJK, Existence and uniqueness in anisotropic conductivity reconstruction with Faraday's law, Inverse Problems and Imaging 17 (2023), 441-462 (preprint,DOI)
[37] M.G. Lee, M.-S. Ko and YJK, Orthotropic conductivity reconstruction with virtual resistive network and Faraday's law, Math. Methods Appl. Sci. 39 (2016), 1183-1196 (preprint, DOI)
[30] M.G. Lee, M.-S. Ko and YJK, Virtual Resistive Network and Conductivity Reconstruction with Faraday's law, Inverse Problems. 30 (2014), no. 12, 125009, 21 pp. (preprint, DOI)
[18] YJK and M.G. Lee, Well-posedness of the conductivity reconstruction from an interior current density in terms of Schauder theory, Quart. Appl. Math. 73 (2015), no.3, 419-433 (preprint, DOI)
[7] YJK, O. Kwon, J.-K. Seo and E. Woo, Uniqueness and convergence of conductivity image reconstruction in magnetic resonance electrical impedance tomography Inverse Problems. 19 (2003) 1213-1225. ( DOI)
[B.1] T.H. Lee, H.S. Nam, M.G. Lee, YJK, E.J. Woo and O.I. Kwon, Reconstruction of Conductivity Using Dual Loop Method with One Injection Current in MREIT Phys. Med. Biol. 55 (2010) 7523--7539.( DOI)

Gas dynamics

[29] YJK, M.G. Lee and M. Slemrod, Thermal creep of a rarefied gas on the basis of non-linear Korteweg-theory, Arch. Ration. Mech. Anal. 214 (2015), no.2, 353-379 (preprint, DOI )
[1] YJK, A self-similar viscosity approach for the Riemann problem in isentropic gas dynamics and the structure of the solutions. Quart. Appl. Math., 59 (2001), no.4, 637-665. (preprint, DOI)

Nonlinear advection and diffusion
Geometric approach

[32] YJK, A geometric one-sided inequality for zero-viscosity limits (preprint)

Diffusion

[60]YJK and Marshall Slemrod, Diffusion with a discontinuous potential: a non-linear semigroup approach, Anal. Theory Appl., (2021) 37, 178--190 (preprint, DOI)
[59] Ho-Youn Kim, YJK, and Hyun-Jin Lim, Heterogeneous discrete kinetic model and its diffusion limit, Kinetic and Related Models (2021) 14(5) 749--765 (preprint, DOI)
[57] YJK and Hyowon Seo, Model for heterogeneous diffusion, SIAM J. Appl. Math., 81 (2021), 335--354. (preprint, DOI)
[22] J. Chung and YJK, Addendum to `Relative Newtonian potentials of radial functions and asymptotics of nonlinear diffusion', SIAM J. Math. Anal., 45 (2013), 728-731. (preprint, DOI)
[21] J. Chung and YJK, Relative Newtonian potentials of radial functions and asymptotics in nonlinear diffusion, SIAM J. Math. Anal. 43 (2011) 1975-1994.(preprint, DOI)
[10] YJK and R. McCann, Potential theory and optimal convergence rates in fast nonlinear diffusion, Journal de Mathematiques Pures et Appliquees 86 (2006), no.1, 42-67 (preprint, DOI )
[9] YJK and R. McCann, Sharp decay rates for the fastest conservative diffusions,C. R. Acad. Sci. Paris Ser. I Math. 341 (2005), 157-162. (preprint, DOI)

Conservation law with convex/nonconvex flux

[41] YJK, Self-similarity of convection-diffusion equations via similarity curves, (preprint)
[17] YJK and Y.-R. Lee, Dynamics in fundamental solutions of a nonconvex conservation law, Proc. R. Soc. Edinb. Sect. A-Math. 146 (2016). no.1, 169--193, (preprint, DOI)
[16] Y. Ha and YJK, Fundamental solutions of a conservation law without convexity,Quart. Appl. Math. 73 (2015), no.4, (preprint, DOI)
[15] M. Kim and YJK, Invariance property of a conservation law without convexity, Indiana Univ. Math. J. 58 (2009) 733-750. (preprint, DOI)
[12] YJK, Potential comparison and asymptotics in scalar conservation laws without convexity, J. Differential Equations 244 (2008), 40-51. (preprint, DOI)
[6] YJK, Asymptotic behavior of solutions to scalar conservation laws and optimal convergence orders to N-waves. J. Differential Equations 192 (2003), no. 1, 202-224. (preprint, DOI)

Burgers / heat equation

[28] J. Chung, YJK and M. Slemrod, An explicit solution of Burgers equation with stationary point source, J. Differential Equations, 257 (2014), no. 7, 2520-2542 (preprint, DOI)
[20] J. Chung, E. Kim and YJK, Asymptotic agreement of moments and higher order asymptotics in the Burgers equation, J. Differential Equations 248 (2010) 2417-2434. (preprint, DOI)
[19] YJK, A generalization of the moment problem to a complex measure space and an approximation technique using backward moments, Discrete Contin. Dyn. Syst. 30 (2011), no. 1, 187-207. (preprint, DOI)
[14] YJK and W.-M. Ni, Higher order approximations in the heat equation and the truncated moment problem. SIAM J. Math. Anal. 40 (2009), no. 6, 2241--2261. (preprint, DOI)
[8] YJK, An Oleinik type estimate for a convection-diffusion equation and the convergence to N-waves, J. Differential Equations 199 (2004), no. 2, 29-289. (preprint, DOI)
[5] YJK and W.-M. Ni, On the rate of convergence and asymptotic profile of solutions to the viscous Burgers equation. Indiana Univ. Math. J. 51 (2002), no.3, 727-752. (preprint, DOI)
[3] YJK and A.E. Tzavaras, Diffusive N-waves and metastability in Burgers equation. SIAM J. Math. Anal. 33 (2001), no.3, 607--633. (preprint, DOI)

FDM for conservation laws

[13] Y. Ha, YJK and Tim Myers, On the numerical solution of a driven thin film equation, J. Comput. Phys. 227 (2008), 7246-7263. (preprint, DOI)
[11] Y. Ha and YJK, Explicit solutions to a convection-reaction equation and defects of numerical schemes, J. Comput. Phys. 220 (2006), 511-531. (preprint, DOI)
[4] YJK, Piecewise self-similar solutions and a numerical scheme for scalar conservation laws. SIAM J. Numer. Anal. 40 (2002), no. 6, 2105-2132. (preprint, DOI)
[2] Shi Jin and YJK, On the computation of roll waves. M2AN Math. Model. Num. Anal., 35 (2001), no.3, 463-480. (preprint, DOI)