TUOC PHAN
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Research Statement
UTK-PDE Lecture Series
CAAM
Summer Meeting
Tuoc Phan
, Professor
Department of Mathematics
University of Tennessee
403 Circle Drive, Knoxville TN 37996-1320
Office
: 211
Ayres Hall
Email
: tphan2 (at) utk dot edu
Phone
: 865-974-4329
$$ \displaystyle{\left[\int_{-\infty}^T\left(\int_{\mathbb{R}^d_+}\big(|u|^p + |Du|^p\big)x_d^\gamma dx\right)^{q/p} dt \right]^{1/q} \leq N\left[\int_{-\infty}^T \left(\int_{\mathbb{R}^d_+} \big(|F|^p +|f|^p\big) x_d^\gamma dx\right)^{q/p} dt \right]^{1/q}}. $$
Welcome to Phan's homepage!
I am a professor at the
Department of Mathematics
,
The University of Tennessee-Knoxville
. I received the bachelor of science degree majoring in mathematics in 2000 from the
University of Science
. I did my graduate study in the
University of Minnesota
(
Twin Cities
-
Minnesota
-
US
) and obtained my Ph.D. degree in 2007. I was a postdoc at
The University of British Columbia
(2007 - 2010), and
The University of Tennessee - Knoxville
(2010 - 2012). My research is in partial differential equations. I study existence, uniqueness, and regularity estimates of solutions. I also work on nonlinear dynamics of solutions, and optimal control problems in mathematical biology. The math formula above is an a-priori estimate of the unknown solution \(u\) of a class singular-degenerate coefficient PDEs. This formula appears in
my recent work
, which is a joint work with
Hongjie Dong
and published
here
by the AMS. Additional information about me can be found in
this article
(in Vietnamese) published by
Vietnamnet
, and also in
an interview video
(in Vietnamese) in the
#toan0mau
series produced by professor
H. V. Tran
.
Preprints
Harnack inequality for singular or degenerate parabolic equations in non-divergence form
(with S. Cho, and J. Fang), (2024), [
arXiv:2409.09437
].
On linear elliptic equations with drift terms in critical weak spaces
(with
H. Kim
and
T.-P. Tsai
), submitted (2023), [
arXiv:2312.11215
].
Recent Accepted/Published Papers
(click
here
for the full list of Phan's publication)
Sobolev estimates for singular-degenerate quasilinear equations beyond the \(A_2\) class
(with
H. Dong
and
Y. Sire
),
The Journal of Geometric Analysis
, Volume 34, article number 286, (2024) [
Journal article
], [
arXiv:2305.07634
].
Nondivergence form degenerate linear parabolic equations on the upper half space
(
H. Dong
and
H. V. Tran
),
Journal of Functional Analysis
(2024), [
Journal article
], [
arXiv:2103.08033
].
On stationary Navier-Stokes equations in the upper-half plane
(with
Adrian D. Calderon
and
Van Le
),
Acta Applicandae Mathematicae
(2024), [
Journal article
], [
arXiv:2306.00319
].
Weighted mixed-norm \(L_p\)-estimates for equations in non-divergence form with singular coefficients: the Dirichlet problem
(with
H. Dong
),
Journal of Functional Analysis
(2023), [
Journal article
], [
arXiv:2103.08033
].
Degenerate linear parabolic equations in divergence form on the upper half space
(with
H. Dong
and
H. V. Tran
),
Transactions of the American Mathematical Society
(2023), [
Journal article
], [
arXiv:2107.08033
].
On trace theorems for weighted mixed norm Sobolev spaces and applications
,
Potentials and Partial Differential Equations: The Legacy of David R. Adams, Vol 8, Advances in Analysis and Geometry
(2023), [
arXiv:2205.04941
].
A boundary layer problem in non-flat domains with measurable viscous coefficients
(with
Dario V. Castillo
),
Studies in Applied Mathematics
, (2022), [
Journal article
].
On parabolic and elliptic equations with singular or degenerate coefficients
(with
H. Dong
),
Indiana University Mathematics Journal
, accepted, [
arXiv
].
Boundary Lebesgue mixed-norm estimates for non-stationary Stokes systems with VMO coefficients
(with
H. Dong
and
D. Kim
),
Communications in Partial Differential Equations
,
https://doi.org/10.1080/03605302.2022.2084627
, arXiv:1910.00380, [
arXiv
].
Editorship
Associate Editor
:
Evolution Equations and Control Theory
(since 06/2021).
Member of Editorial Board
:
Electronic Journal of Differential Equations
(since 07/2021).
Editor (member)
:
Nonlinear Dispersive Waves and Fluids
,
Contemporary Mathematics
, Volume: 725, 2019.
Others (for Vietnamese)
My interview (inVietnamese) with
Vietnamnet
about virtual teaching is
here
.
An article about me
(in Vietnamese) in
Vietnamnet
.
Phan's interview
(in Vietnamese) in
#toan0mau
series.
My lecture in
Diễn Giải Toán Học 2020
:
video
(in Vietnamese) and
lecture notes
.
Coming Up