My current interests generally fall within the analysis of evolutionary partial differential equations in chemistry, biology, and physics, mainly including
Topic 1: Kinetic theory: From Boltzmann equations to Cross-diffusion systems, High friction limits;
Topic 2: Chemotaxis systems: Global existence and blow up, large-time behaviours, singular limits, etc.; and
Topic 3: Fast reaction limits in reaction-diffusion systems, their convergence rates and geometrical theory of dynamical systems.
My research is being developed in collaboration with Ass-Prof. Bao Quoc Tang (University of Graz), Prof. Christian Kuehn (Technical University of Munich), Prof. Laurent Desvillettes (Université Paris Cité), Prof. Jeffrey Morgan (University of Houston), Prof. Hong Duong (University of Birmingham), Assoc. Prof. Le Trong Thanh Bui (Vietnam National University HCM City), Dr. Masaaki Mizukami (Kyoto University Of Education), etc.
PREPRINTS:
[35] Laurent Desvillettes, Christian Kuehn, Jan-Eric Sulzbach, Tang Quoc Bao, BNT, Slow Manifolds for PDE with Fast Reactions and Small Cross Diffusion, arXiv:2501.16775, 51 pages, 2025.
[34] Cordula Reisch, BNT, and Juan Yang. Rigorous fast signal diffusion limit and convergence rates with the initial layer effect in a competitive chemotaxis system, arXiv:2405.17392, 48 pages, 2024.
[33] BNT, Juan Yang, Global solvability for doubly degenerate nutrient taxis system with a wide range of bacterial responses in physical dimension, arXiv:2508.03268, 45 pages, 2025.
PUBLICATIONS:
On mathematical biology
[32] L.T. Thanh Bui, T.K. Loan Huynh, Q. Bao Tang, BNT. Parabolic-elliptic and indirect-direct simplifications in chemotaxis systems driven by indirect signalling, Calculus of Variations and Partial Differential Equations, Volume 65, article number 76, 2026.
[31] J. Morgan, C. Soresina, B.Q. Tang, BNT. Singular limit and convergence rate via projection method in a model for plant-growth dynamics with autotoxicity, Journal of Differential Equations, Volume 452, 113797, 37 pages, 2025.
[30] B.Q. Tang, BNT. Rigorous derivation of Michaelis-Menten kinetics in the presence of slow diffusion. SIAM Journal on Mathematical Analysis, Volume 56, Issue 5, 2024.
On inverse problems
[29] H.T. Nguyen, BNT. Inverse initial-value problems for time-fractional diffusion equations in fractional Sobolev spaces. Mathematische Nachrichten, 2023.
[28] D.K. Tran, BNT, H.T. Nguyen. Final value problem governed by a class of time-space fractional pseudo-parabolic equations with weak nonlinearities, Math. Methods Appl. Sci., 47 (2023), no. 6, 5307–5328.
[27] BNT, E. Nane, H.T. Nguyen. On a terminal value problem for stochastic space-time fractional wave equations. Math. Methods Appl. Sci., 46 (2023), no. 1, 1206–1226.
[26] BNT, V.T. Vo. Global existence and continuous dependence on parameters for space-time fractional pseudo-parabolic inclusion, J. Nonlinear Convex Anal., 23 (2022), no. 7, 1469–1485.
[25] T. Caraballo, BNT, N.T. Tran, H.T. Nguyen. On a stochastic nonclassical diffusion equation with standard and fractional Brownian motion, Stoch. Dyn., 22 (2022), Number 2, Paper no. 2140011, 45 pp.
[24] H.T. Nguyen, D. Lesnic, N.T. Tran, BNT. Regularization of the backward stochastic heat conduction problem, J. Inv. Ill-Posed Problems, 30 (2022), no. 3, 351–362.
[23] BNT, H.T. Nguyen. Existence of mild solutions to semilinear fractional evolution equation using Krasnoselskii fixed point theorem, Filomat, 36 (2022), no. 4, 1099–1112.
[22] H.Q.N. Danh, D.L. Le, D. O'Regan, BNT, H.T. Nguyen. Identification of the right-hand side in a bi-parabolic equation with final data, Appl. Anal., 101 (2022), no. 4, 1157–1175.
[21] BNT, N.T. Tran, D. O’regan, H.T. Nguyen. On inverse initial value problems for the stochastic strongly damped wave equation, Appl. Anal., 101 (2022), no. 2, 527–544.
[20] BNT, H.T. Nguyen, S. Rathinasamy, D. O'Regan. Analysis of nonlinear fractional diffusion equations with a Riemann-Liouville derivative, Evol. Equ. Control Theory, 11 (2022), no. 2, 439–455.
[19] T. Caraballo, BNT, H.T. Nguyen, R. Wang, On a nonlinear Volterra integrodifferential equation involving fractional derivative with Mittag-Leffler kernel, Proc. Am. Math. Soc., 149 (2021), no. 8, 3317–3334.
[18] BNT, V.T. Vo, Z. Hammouch, H.C. Nguyen. Stability of a class of problems for time-space fractional pseudo-parabolic equation with datum measured at terminal time, Appl. Numer. Math., 167 (2021), 308–329.
[17] T. Caraballo, BNT, N.T. Tran, H.T. Nguyen. On initial value and terminal value problems for subdiffusive stochastic Rayleigh-Stokes equation, Discrete Contin. Dyn. Syst. - B, 26 (2021), no. 8, 4299–4323.
[16] BNT, T. Caraballo, H.T. Nguyen, Y. Zhou. Existence and regularity results for terminal value problem for nonlinear fractional wave equations, Nonlinearity, 34 (2021), no. 3, 1448–1502.
[15] BNT, H.L. Nguyen, V.A. Vo, H.T. Nguyen, Y. Zhou. Existence and regularity of inverse problem for the nonlinear fractional Rayleigh‐Stokes equations, Math. Methods Appl. Sci., 44 (2021), no. 3, 2532–2558.
[14] T.B. Tran, H.T. Nguyen, BNT. Holder continuity of mild solutions of space-time fractional stochastic heat equation driven by colored noise, Eur. Phys. J. Plus, 136 (2021), 21 pp.
[13] H.T. Nguyen, D. O’Regan, BNT. Continuity with respect to fractional order of the time fractional diffusion-wave equation, Evol. Equ. Control Theory, 9 (2020), no. 3, 773–793.
[12] BNT, D. Baleanu, T.M.D. Le, H.T. Nguyen. Regularity results for fractional diffusion equations involving fractional derivative with Mittag-Leffler kernel, Math. Methods Appl. Sci., 43 (2020), no. 12, 7208–7226.
[11] BNT, H.T. Nguyen, Y. Zhou, D. O'Regan. On existence and regularity of a terminal value problem for the time fractional diffusion equation, Inverse Problems, 36 (2020), no. 5, 055011, 41 pp.
[10] H.T. Nguyen, BNT, D. Baleanu, D. O'regan. On well-posedness of the sub-diffusion equation with new derivative model, Commun. Nonlinear Sci. Numer. Simul., 89 (2020), 105332, 26 pp.
[9] BNT, V.A. Vo, Y. Zhou, T.H. Nguyen. On a final value problem for fractional reaction-diffusion equation with Riemann-Liouville fractional derivative, Math. Methods Appl. Sci., 43 (2020), no. 6, 3086–3098.
[8] BNT, Y. Zhou, D. O'regan, H.T. Nguyen. On a terminal value problem for pseudoparabolic equations involving Riemann-Liouville fractional derivatives, Appl. Math. Lett., 106 (2020), 106373, 9 pp.
[7] BNT, H.T. Nguyen, M. Kirane. Regularization of sideways problem for a time fractional diffusion equation with nonlinear source, J. Inv. Ill-Posed Problems, 28 (2020), no. 2, 211–235.
[6] H.T. Nguyen, BNT, N.H. Le, M. Kirane. Existence and uniqueness of mild solution of time-fractional semilinear differential equations with a nonlocal final condition, Comp. Math. Appl., 78 (2019), 1651–1668.
[5] H.T. Nguyen, A. Debbouche, BNT. Existence and regularity of final value problems for time fractional wave equations, Comput. Math. Appl., 78 (2019), no. 5, 1396–1414.
[4] D.P. Nguyen, H.T. Nguyen, D. Baleanu, BNT. On Cauchy problem for nonlinear fractional differential equation with random discrete data, Appl Math Comput., 362 (2019), 124458, 16 pp.
[3] BNT, H.T. Nguyen, D. O’Regan. Existence and uniqueness of mild solutions for a final value problem for nonlinear fractional diffusion systems, Commun. Nonlinear Sci. Numer. Simul., 78 (2019), 104882, 13 pp.
[2] H.T. Nguyen, N.H. Le, BNT, Y. Zhou. On a backward problem for nonlinear fractional diffusion equations, Appl. Math. Lett., 92 (2019), 76–84.
[1] H.T. Nguyen, BNT, S. Tatar, D.L. Le. Recovery of the solute concentration and dispersion flux in an inhomogeneous time fractional diffusion equation, J. Comput. Appl. Math., 342 (2018), 96–118.
FULL PUBLICATIONS: Please look at the MathSciNet Link.