Research Interests

My research focuses on nonlinear partial differential equations and the calculus of variations, with an emphasis on effective boundary laws for nonlinear flow systems and quasiconvex variational problems in BV. I am particularly interested in low-regularity phenomena, weak formulations, and the emergence of macroscopic behavior from microscopic structures.

Publications and Preprints

11. Generalized Navier-like boundary conditions for nonlinear flow systems (with Jean-Luc Thiffeault), In preparation.

10. Lower-Order Regularity for Relaxed Minimizers under (1, q)-growth, Forthcoming.

9. Quasiconvex functionals with (1, q)-growth in BV, Submitted, 2026. 37 pp.

8. Existence and uniqueness of positive solution for a fractional p-Laplacian equation of logistic-type with harvesting terms (with Khieu T. Tran), Mediterranean Journal of Mathematics, Issue 3, Volume 23, Article No.: 99 (2026), DOI.

7. Stability estimates for nonlinear backward diffusion equations with superposition operators of mixed orders and time-dependent coefficient (with Khieu T. Tran, and Khanh Q. Tra), Inverse Problems, Issue 3, Volume 42 (2026), DOI.

6. On a bistable delayed nonlinear reaction-diffusion equation with a two-phase free boundary: Semi-wave and its numerical simulation, Studies in Applied Mathematics, Issue 2, Volume 154 (2025), DOI.

5. Monotonicity for quasilinear Elliptic problems with a sign-changing nonlinearity in half-planes (with Phuong Le, and Chi T. Vo), Comptes Rendus Mathématique. Académie des Sciences. Paris, Volume 363 (2025), pp. 69-87, DOI.

4. Dynamics for advective-cooperative system with free boundaries in a Nondegenerate Epidemiological Model, Nonlinear Dynamics, Issue 3, Volume 113 (2024), pp. 2941–2968, DOI.

3. On the fractional p-q Laplace operator with weights  (with Khieu T. Tran), Applicable Analysis, Issue 7, Volume 104 (2023),  pp.1314-1335, DOI.

2.  Dynamics for a two-phase free boundary system in an Epidemiological Model with couple nonlocal dispersals (with Hung  H. Vo), Journal of Differential Equations, Volume 335 (2022), pp.398–463, DOI.

1.  Spreading of two competing species in advective environment governed by free Boundaries with a given moving boundary (with Trong D. Dang, Hung  H. Vo), Vietnam Journal of Mathematics, Issue 4, Volume 49 (2021), pp.1199–1225, DOI.

0. Principal eigenvalue and positive solutions for fractional p-q Laplace operator in quantum field theory (unpublished) (2020), arXiv:2006.03233.