Welcome to my page!
I am Seonghak Kim(김성학 in Korean), an Associate Professor in the Department of Mathematics at Kyungpook National University, Daegu, South Korea. My primary interests lie in nonlinear partial differential equations and direct methods in the calculus of variations.
You can reach me through my permanent email address: shkim17 (at) knu (dot) ac (dot) kr.
Research Interests
1. Parabolic and Hyperbolic PDEs
2. Convex Integration and Applications
3. Elasticity, Population Dynamics
Employment
1. Associate Professor, October 2022 -- Present
Chair of the Department, February 2021 -- January 2023
Assistant Professor, September 2017 -- September 2022
Department of Mathematics
Kyungpook National University, Daegu, South Korea
2. Visiting Scholar, January 2023 -- February 2024
Department of Mathematics
Michigan State University, East Lansing, MI, USA
3. Postdoctoral Fellow, September 2015 -- June 2017
Institute for Mathematical Sciences
Renmin University of China, Beijing, China
Education
1. Ph.D. in Mathematics, 2015
Michigan State University, East Lansing, MI, USA
Adviser: Dr. Baisheng Yan
2. M.S. in Mathematics, 2009
KAIST, Daejeon, South Korea
Adviser: Dr. U Jin Choi
(Military Service, July 2005 -- July 2007)
3. B.S. in Mathematics, 2005
Sogang University, Seoul, South Korea
Grants
1. National Research Foundation of Korea, Mar. 2018 -- Feb. 2022
2. Basic Research Laboratory, National Research Foundation of Korea, 2020 -- 2023
3. National Research Foundation of Korea, Jun. 2022 -- Feb. 2025
4. Basic Research Laboratory, National Research Foundation of Korea, 2023 -- 2026
Publications and Preprints
Journal Articles
1. Radial weak solutions for the Perona-Malik equation as a differential inclusion (with Baisheng Yan), J. Differential Equations, 258 (6) (2015), 1889-1932. (PDF)
2. Convex integration and infinitely many weak solutions to the Perona-Malik equation in all dimensions (with Baisheng Yan), SIAM J. Math. Anal., 47 (4) (2015), 2770-2794. (PDF)
3. On a gradient maximum principle for some quasilinear parabolic equations on convex domains, Proc. Amer. Math. Soc., 145 (3) (2017), 1203-1208. (PDF)
4. On Lipschitz solutions for some forward-backward parabolic equations. II: the case against Fourier (with Baisheng Yan), Calc. Var. Partial Differential Equations, 56 (67) (2017). (PDF)
5. Strichartz estimates for the magnetic Schrödinger equation with potentials V of critical decay (with Youngwoo Koh), Comm. Partial Differential Equations, 42 (9) (2017), 1467-1480. (PDF)
6. Rate of convergence for one-dimensional quasilinear parabolic problem and its applications, J. Differential Equations, 264 (1) (2018), 82-97. (PDF)
7. On Lipschitz solutions for some forward-backward parabolic equations (with Baisheng Yan), Ann. Inst. H. Poincaré Anal. Non Linéaire, 35 (1) (2018), 65-100. (PDF)
8. Convex integration for scalar conservation laws in one space dimension (with Hoang-Hung Vo), SIAM J. Math. Anal., 50 (3) (2018), 3122-3146. (PDF)
9. On asymptotic behavior and energy distribution for some one-dimensional non-parabolic diffusion problems (with Baisheng Yan), Nonlinearity, 31 (6) (2018), 2756–2808. (PDF)
10. On one-dimensional forward-backward diffusion equations with linear convection and reaction (with Baisheng Yan), J. Differential Equations, 266 (2-3) (2019), 1578-1604. (PDF)
11. Two-phase solutions for one-dimensional non-convex elastodynamics (with Youngwoo Koh), Arch. Ration. Mech. Anal., 232 (1) (2019), 489-529. (PDF)
12. Liouville type result and long time behavior for Fisher-KPP equation with sign-changing and decaying potentials (with Hoang-Hung Vo), J. Differential Equations, 268 (10) (2020), 5629-5671. (PDF)
13. Convex integration with linear constraints and its applications, J. Math. Anal. Appl., 487 (2) (2020), 124028, 29 pp. (PDF)
14. Exponential decay for quasilinear parabolic equations in any dimension (with Jian-Wen Sun), Discrete Contin. Dyn. Syst. Ser. B, 27 (10) (2022), 5411-5418. (PDF)
15. Fine phase mixtures in one-dimensional hyperbolic-elliptic problem (with Hyung Jun Choi), J. Differential Equations, 363 (2023), 195-242. (PDF)
16. Adhesion and volume filling in one-dimensional population dynamics under Dirichlet boundary condition (with Hyung Jun Choi & Youngwoo Koh), Proc. Roy. Soc. Edinburgh Sect. A, to appear.
Preprints
17. Weak solutions to a hyperbolic-elliptic problem, submitted.
18. Time splitting method for nonlinear Schrodinger equation with rough initial data in L^2 (with Hyung Jun Choi & Youngwoo Koh), submitted.
19. Adhesion and volume filling in one-dimensional population dynamics II: no-flux boundary condition (with Hyung Jun Choi & Youngwoo Koh), preprint.
20. On integral convexity, variational solutions and nonlinear semigroups (with Baisheng Yan), submitted.
Works in preparation
21. (with Hyung Jun Choi & Youngwoo Koh)
22. (with Baisheng Yan)
23. (with no others)
24. (with Hyung Jun Choi & Youngwoo Koh)
25. (with Hyung Jun Choi)
26. (with Hyung Jun Choi & Youngwoo Koh)
Last updated on 12/12/2023.