Research Interests

My research lies in nonlinear partial differential equations and the calculus of variations, with current emphasis on nonlinear flow systems, generalized boundary effects, and weak formulations in low-regularity settings.  My earlier work includes nonlinear diffusion, free boundary problems, and fractional operators.

Publications

My publications reflect earlier work in nonlinear PDE and free boundary problems, as well as current research in nonlinear fluid dynamics and the calculus of variations.

11. Generalized Navier-like boundary conditions for nonlinear flow systems (with Jean-Luc Thiffeault), in preparation 2026.

10. Weak Euler-Lagrange equations for relaxed minimizers of quasiconvex functionals in BV, in preparation 2026.

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, (2026), [Journal article].

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), [Journal article].

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), [Journal article].

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, [Journal article].

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

3. On the Fractional P-Q Laplace operator with weights  (with Khieu T. Tran), Applicable Analysis, Issue 7, Volume 104 (2023),  pp.1314-1335, [Journal article].

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, [Journal article].

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, [Journal article].

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 Principal eigenvalue and positive solutions for Fractional p-q Laplace operator in quantum field theory (unpublished) (2020), [arXiv:2006.03233].