Career • 2019.12-present Research Assistant Professor, ShanghaiTech University • 2014.4-2019.9 Researcher & Lecturer, Faculty of Mathematics and Statistics, Ton Duc Thang University
Education • December 2013, Ph.D in Mathematics, Universit´e Francois Rabelais de Tours, France • July 2009, Master in Mathematics, Universit´e d´Orl´eans, France • July 2006, B.S. in Mathematics, Ho Chi Minh University of Science, Vietnam
Research Interest 0.1. Partial Differential Equations • Hamilton-Jacobi parabolic equation with an absorption term of gradient: decay estimates; regularity; blow-up on the boundary, large solutions; removable singularity; the initial trace; and renormalized solution. • Singular solutions of quasi-linear parabolic equations: The existence and uniqueness of fundamental solutions, very singular solutions, and large solutions; short time and long time behaviour of singular solutions. • Parabolic equations with a singular absorption: Gradient estimates (Bernstein’s technique); regularity; global quenching phenomenon, free boundary, blow-up of solutions. • Fractional parabolic equations: decay estimates, regularity, extinction of solutions. 0.2. Functional inequalities. Gagliardo-Nirenberg interpolation inequalities; Fractional Sobolev embedding; the Brezis-Gall¨ouet-Wainger's inequality,... 0.3. Operator theory. The boundedness and compactness characterization of integral commutators associated with a singular kernel of Calder´on Zygmund type. on strictly pseudoconvex domains in Cn.
Selected Publications [1] M. F. Bidaut-V´eron and N. A. Dao, Isolated initial singularities for the viscous HamiltonJacobi equation, Advances in Differential Equations, 17 (2012), 903-934. [2] M. F. Bidaut-V´eron and N. A. Dao, L∞-estimates and uniqueness results for nonlinear parabolic equations with gradient absorption terms, Nonlinear Analysis, 91 (2013), 121-152. [3] M. F. Bidaut-V´eron and N. A. Dao, Initial trace results for viscous Hamilton-Jacobi equation, Advanced Nonlinear Studies, 15 (2015), 889-921. [4] N. A. Dao and J. I. Diaz, A gradient estimate to a degenerate parabolic equation with a singular absorption term: The global quenching phenomena, Journal of Mathematical Analysis and Applications, 437 (2016), 445-473. [5] N. A. Dao, J. I. Diaz and Paul Sauvy, Quenching phenomenon of singular parabolic problems with L1 initial data, Elec. Jour. Diff. Equa., 2016 (2016), No. 136, 1-16. [6] N. A. Dao, Uniqueness of very singular solution of nonlinear degenerate parabolic equations with absorption for Dirichlet boundary condition, Elec. Jour. Diff. Equa., 2016 (2016), No. 299, 1-8. [7] N. A. Dao and J. I. Diaz, Existence and uniqueness of singular solutions of p-Laplacian with absorption for Dirichlet boundary condition, Proc. Amer. Math. Soc., 145 (2017), 52355245. [8] L. T. Bui, N. A. Dao and J. I. Diaz, Critical case for the viscous Cahn-Hilliard equation, Elec. Journal of Differential Equations, 2017 (2017), No. 176, 1-8. [9] N. A. Dao and J. I. Diaz, The extinction versus the blow-up: Global and non-global existence of solutions of source types of degenerate parabolic equations with a singular absorption, Journal of Differential Equations, 263 (2017), 6764-6804. [10] N. A. Dao, Instantaneous shrinking of compact support of solutions of semi-linear parabolic equations with singular absorption, Annals of the University of Craiova, Mathematics and Computer Science Series, 44 (2017), 156-168. [11] N. A. Dao and Quoc-Hung Nguyen, Nonstationary Navier-Stokes equations with singular time-dependent external forces, C. R. Acad. Sci. Paris, Ser. I, 355 (2017), 966-972. [12] N. T. Duy and N. A. Dao, Blow-up of solutions to singular parabolic equations with nonlinear sources, Elec. Jour. Diff. Equa., 2018 (2018), No. 48, 1-12. [13] N. A. Dao and Q. H. Nguyen, Brezis-Gallouet-Wainger type inequality with critical fractional Sobolev space and BMO, Comptes Rendus Mathematique, 356 (2018), 747-756. [14] N. A. Dao, J. I. Diaz and Q. H. Nguyen, Generalized Gagliardo-Nirenberg inequalities using Lorentz spaces, BMO, H¨older spaces and Fractional Sobolev spaces, Nonlinear Analysis, 173 (2018), 146-153. [15] N. A. Dao, N. V. Bay and D. P. Tan, A quenching result of weak solutions of semi-linear parabolic equations, Annals of the University of Craiova, Mathematics and Computer Science Series, 45 (2018), 223-227. [16] N. A. Dao, N. N. Trong, L. X. Truong, Besov-Morrey space associated with Hermite operators and applications to fractional Hermite equations, Elec. Jour. Diff. Equa., 2018 (2018), No. 187, 1-14. [17] N. A. Dao, J. I. Diaz and Huynh Van Kha, Complete quenching phenomenon and instantaneous shrinking of compact support of degenerate parabolic equations with nonlinear absorption, Proceedings of the Royal Society of Edinburgh, Section A: Mathematics, 149, 1323–1346, 2019. [18] N. A. Dao, N. T. N. Hanh, T. M. Hieu and H. B. Nguyen Interpolation Inequalities between Lorentz space and BMO: The endpoint case (L1,∞,BMO), Elec. Jour. of Diff. Equa., 2019 (2019), No. 56, 1-4. [19] Nguyen Anh Dao, Jesus Ildefonso D´ıaz, Energy and large time estimates for nonlinear porous medium flow with nonlocal pressure in RN, In a revision on Arch. Rat. Mech. Anal., 2019. [20] Nguyen Anh Dao, Morrey boundedness and compactness characterizations of integral commutators with singular kernel on strictly pseudoconvex domain in CN , Submitted to JMAA, 2019. [21] Nguyen Anh Dao, Xuan Thinh Duong, and Ly Kim Ha, Commutators of CauchyFantappi`e type integrals on generalized Morrey spaces on domains of finite type, Submitted to Jour. Geo. Anal., 2019. [22] Nguyen Anh Dao, Jesus Ildefonso D´ıaz, and Quoc-Hung Nguyen, Fractional Sobolev inequalities revisited: the maximal function approach, To appear in Rend. Lincei Mat. Appl. [23] Nguyen Anh Dao, Jesus Ildefonso D´ıaz, and Quan Ba Hong Nguyen, Pointwise Gradient Estimates in Multi-dimensional Slow Diffusion Equations with a Singular Quenching Term, Adv. Nonlinear Stud. 2020.
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Email: anhnguyenmaths@gmail.com Office: S512, School of Creativity & Arts |
