Tuoc Phan’s list of publication

                      I.     Journal Papers

1.      Gradient estimates for weak solutions of linear elliptic systems with singular-degenerate coefficients (with Dat Cao and Tadele Mengesha) 18 pp., submitted, [arXiv].

2.      Lorentz estimates for weak solutions of quasi-linear parabolic equations with singular divergence-free drifts, 35p., submitted, [arXiv].

3.      Regularity estimates for BMO-weak solutions of quasi-linear equations with inhomogeneous boundary conditions, 24pp., submitted,  [arXiv].

4.      Interior gradient estimates for weak solutions of quasi-linear p-Laplacian type equations, 17pp., submitted, [arXiv].

5.      Weighted Calderon-Zygmund estimates for weak solutions of quasi-linear degenerate elliptic equations, 28 pp., submitted,  [arXiv].

6.      Weighted W1,p-estimates for weak solutions of degenerate elliptic equations with coefficients degenerate in one variable (with and Tadele Mengesha), 36 pp., submitted, [arXiv].

7.      Free energy in a mean field of Brownian particles (with X. Chen), submitted, 25 pp. (preprint).

8.      Weighted W1,p-estimates for weak solutions of degenerate and singular elliptic equations (with Dat Cao and Tadele Mengesha), 36pp.,  to appear in Indiana University Mathematics Journal, [arXiv].

9.      Regularity gradient estimates for weak solutions of singular quasi-linear parabolic equations, Journal of Differential Equations 263 (2017) 8329-8361, doi.org/10.1016/j.jde.2017.08.043, [Journal paper], [arXiv].

10.   Local W1,p –regularity estimates for weak solutions of parabolic equations with singular divergence-free drifts, Electronic Journal of Differential Equations, Vol. 2017 (2017), No. 75, pp. 1-22 [Journal paper], [arXiv].

11.   Advection control in parabolic PDE systems for competitive populations (with K. De Silva, and & S. Lenhart), 23 pp., Discrete and Continuous Dynamical Systems, Series B, Vol. 22, Issue 3 (2017), 1049 – 1072, [Journal paper], [MathSciNet Review].

12.   Asymptotic stability of solitary waves in generalized Gross--Neveu model (with Andrew Comech and Atanas Stefanov), Annales de l’Institut Henri Poincare (C) Non Linear Analysis, Vol. 34, Issue 1 (2017), 157-196,  [Journal paper], [arXiv preprint], [MathSciNet Review].

13.   On small energy stabilization in the NLKG with a trapping potential (with Scipio Cuccagna, and Masaya Maeda), Nonlinear Analysis, Vol. 146 (2016), 32-58, [Journal paper], [arXiv preprint], [MathSciNet].

14.   Interior gradient estimates for quasi-linear elliptic equations (with Truyen Nguyen), Calculus of Variations and Partial Differential Equations, Vol. 55, no. 3 (2016) [Journal paper] [arXiv preprint], [MathSciNet Review].

15.   Local gradient estimates for degenerate elliptic equations (with Luan T. Hoang and Truyen V. Nguyen), Adv. Nonlinear Stud. 16 (2016), no. 3, 479–489,  [Journal paper], [arXiv preprint], [MathSciNet Review].

16.   Gradient estimates and global existence of smooth solutions for a system of cross-diffusion equations (with Luan T. Hoang and Truyen V. Nguyen), SIAM J. of Math. Analysis , Vol. 47, Issue 3 (2015), 2122-  2177 [Journal paper], [arXiv preprint], [MathSciNet Review].

17.   Properties of generalized Forchheimer flows in porous media, (with Thinh Kieu and Luan Hoang), Problemy Matematicheskogo Analiza, volume 76 (2014), 133 – 194 (in Russian), and (English translation) "Journal of Mathematical Sciences", vol. 202 (2014) No. 2, 259 - 332. [Journal paper], [IMA preprint] [arXiv preprint], [MathSciNet Review].

18.   Stationary Navier-Stokes equations with critically singular external forces: Existence and stability results (with Nguyen Cong Phuc), Adv. Math. 241 (2013), 137–161 [Journal paper] [arXiv preprint ], [MathSciNet Review].

19.   Optimal control of advection direction on reaction - diffusion population models (with H. Finotti & S. Lenhart), Evol. Equ. Control Theory 1 (2012), no. 1, 81–107 [Journal paper] [Preprint version], [MathSciNet Review]

20.   Normal form for symmetry breaking bifurcation in the Gross-Pitaevskii equation (with D.E. Pelinovsky),  J. Differential Equations 253 (2012), no. 10, 2796–2824, [Journal paper], [Arxiv preprint], [MathSciNet Review].

21.   Small Solutions of nonlinear Schrödinger equations near first excited states (with Kenji Nakanishi and Tai-Peng Tsai), J. Funct. Anal. 263 (2012), no. 3, 703–781 [Journal paper], [Preprint version], [MathSciNet Review].

22.   A Remark on global existence of solutions of shadow systems, Z. Angew. Math. Phys. 63 (2012), no. 2, 395–400, [Journal paper];  [Preprint], [MathSciNet Review].

23.   Stable directions for degenerate excited states of nonlinear Schödinger equations (with Stephen Gustafson) SIAM J. of Math. Analysis, Vol. 43, Issue 4 (2011), pp. 1716-1758, [Journal paper], [arXiv preprint],  [MathSciNet Review]

24.   On global existence of solutions to a cross-diffusion system, J. Math. Anal. App. Vol 343, Issue 2, 15 July 2008, pp. 826-834 [Journal paper], [IMA preprint], [MathSciNet Review].

25.   On global existence of solutions to Shigesada-Kawasaki-Teramoto cross-diffusion systems in domains of arbitrary dimensions, Proc. Amer. Math. Soc. 135 (2007), pp. 3933-3941 [Preprint], [Journal paper], [MathSciNet Review].

26.   Lagrange multipliers for functions derivable along directions in linear subspace (with Le Hai An, Pham Xuan Du and Duong Minh Duc, Proc. Amer. Math. Soc. 133 (2005), no. 2, pp. 595—604 [Journal paper], [MathSciNet Review].

27.   Topological degree for a class of operators and applications (with Duong Minh Duc and Nguyen Hoang Loc) Nonlinear Analysis Vol 57 (2004), Issue 4 [Journal paper], [MathSciNet Review].

28.   Generalized zeros of operators and applications (with Duong Minh Duc and Nguyen Hoang Loc) Vietnam J. Math. 32 (2004), Special Issue, pp. 87—96 [Journal paper], [MathSciNet Review].

                      II.     Ongoing Projects

1.      On W1,p-regularity estimate for a class of generalized singular Stokes systems and its applications to the Navier-Stokes equations.

2.      Global regularity gradient estimates for weak solutions of a class of quasi-linear parabolic p-Laplacian type equations.

                    III.     Others (un-published work)

1.   Ljusternik theorem for non-differentiable functionals, B.S. Thesis, University of Science , Vietnam National Unversity - Ho Chi Minh City (2000) [pdf].

2.   On Global Existence of Solutions to a Cross-Diffusion System, Ph.D. Thesis, University of Minnesota , July 2007 [pdf].

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