Tuoc Phan’s homepage
227 Ayres hall, 1403 Circle Drive
Knoxville, TN 37996
Office: 225 Ayres hall
Email: tphan2 at utk.edu
Fax: (865) - 974 - 6576
Research interests: Partial Differential Equations
v Existence uniqueness and regularity theory
nonlinear, elliptic parabolic equations and system of equations, nonlinear
p-Laplacian equations, equations with singular degenerate coefficients,
v Nonlinear dynamics in nonlinear dispersive equations: Asymptotical stability of solitons
in Dirac equations, Klein-Gordon equations, and Schrödinger equations.
v Optimal control and its applications in mathematical biology: Population (cells, chemical concentration) dynamics in heteronomy. My work provides potential optimal methods for treatment and managements.
Curriculum vitae: [PDF], Research statement: [PDF], Teaching statement: [PDF]
1. Regularity theory for parabolic equations with singular degenerate coefficients (with H. Dong), Calculus of Variations and Partial Differential Equations, accepted, [arXiv].
2. Existence uniqueness and regularity theory for elliptic equations with complex valued potentials (with G. Todorova and B. Yordanov), Discrete and Continuous Dynamical Systems – Series A, [Journal article] [preprint].
3. Weighted mixed-norm L_p-estimates for elliptic and parabolic equations in non-divergence form with singular degenerate coefficients (with H. Dong), Revista Matemática Iberoamericana, accepted, arXiv:1811.06393 [arXiv].
4. Liouville type theorems for 3D stationary Navier-Stokes equations in weighted mixed-norm Lebesgue spaces, Dynamics of Partial Differential Equations, Vol 17, no. 3 (2020), 229-243 [Journal article] [arXiv]
5. On well-posedness of 2D dissipative quasi-geostrophic equation in critical mixed norm Lebesgue spaces (with Y. Sire), Analysis in Theory and Applications, 36 (2) (2020), 111-127 [Journal article] [preprint]
7. Weighted Calderon-Zygmund estimates for weak solutions of quasi-linear degenerate elliptic equations, Potential Analysis, 52 (2020), 393-425, DOI: 10.1007/s11118-018-9737-z [Author shared link][Journal article], [arXiv].
8. Free energy in mean field of Brownian particle (with X. Chen), Discrete and Continuous Dynamical Systems – Series A, 39 (2019), no. 2, 747-769, [Journal article] [preprint].
9. Weighted W1,p-estimates for weak solutions of degenerate elliptic equations with coefficients degenerate in one variable (with Tadele Mengesha), Nonlinear Analysis, Vol. 179 (2019), p. 184-236 https://doi.org/10.1016/j.na.2018.08.012 [Journal article][arXiv].
10. Lorentz estimates for weak solutions of quasi-linear parabolic equations with singular divergence-free drifts, Canadian Journal of Mathematics, Vol 71, Issue 4 (2019), 937-982, [Journal version], [preprint]
Complete list of publication: list of publication and preprints
Grants: Simons collaboration (2015-2020), grant #354889.
1. Special Session on “Nonstandard elliptic and parabolic regularity theory with applications”, AMS meeting Oct 10 -11, 2020, Chattanooga, TN
2. Conference of Analysis and Applied Mathematics, Sai Gon University, December 17 - 18, 2020, Ho Chi Minh City, Vietnam
CAAM’s information: Conference on Analysis and Applied Mathematics.