Daniel Phillips

Education

• University of Minnesota, 1981

My Spring Office Hours are Tuesday 1:30- 2:30, Thursday 10:30-11:30 or by appointment.

I teach MA 44200H Honors Real Analysis II and MA 26600-402 Ordinary Differential Equations during Spring 2020. Their course pages are available on Brightspace .

My research concerns partial differential equations motivated from problems in materials science and condensed matter physics, in particular applications to liquid crystals, polymers, composites, and superconductors. Currently I am working on analyzing mathematical models for nematic and smectic liquid crystals.

Preprints

• Dynamic Analysis of Chevron Structures in Liquid Crystal Cells ; Lidia Mrad and Daniel Phillips

• Numerical Analysis and Simulation for a Generalized Planar Ginzburg-Landau Equation in a Circular Geometry ; Sean Colbert-Kelly, Geoffrey B. Mcfadden, Daniel Phillips and Jie Shen

Selected Publications

• Patricia Bauman, Daniel Phillips, and Changyou Wang. Higher dimensional Ginzburg-Landau equations under weak anchoring boundary conditions . J. Funct. Anal. , 276(2):447–495, 2019.
• Lidia Mrad and Daniel Phillips. Dynamic analysis of chevron structures in liquid crystal cells . Molecular Crystals and Liquid Crystals , 647(1):66-91, 2017.
• Sean Colbert-Kelly, Geoffrey B. McFadden, Daniel Phillips, and Jie Shen. Numerical analysis and simulation for a generalized planar Ginzburg-Landau equation in a circular geometry . Commun. Math. Sci. , 15(2):329–357, 2017.
• Patricia Bauman and Daniel Phillips. Regularity and the behavior of eigenvalues for minimizers of a constrained Q" role="presentation"> Q Q -tensor energy for liquid crystals . Calc. Var. Partial Differential Equations , 55(4):Art. 81, 22, 2016.
• Lei Z. Cheng and Daniel Phillips. An analysis of chevrons in thin liquid crystal cells . SIAM J. Appl. Math. , 75(1):164–188, 2015.
• Patricia Bauman, Daniel Phillips, and Jinhae Park. Existence of solutions to boundary value problems for smectic liquid crystals . Discrete Contin. Dyn. Syst. Ser. S , 8(2):243–257, 2015.
• Sean Colbert-Kelly and Daniel Phillips. Analysis of a Ginzburg-Landau type energy model for smectic C∗" role="presentation"> C ∗ C∗ liquid crystals with defects . Ann. Inst. H. Poincar'e Anal. Non Lin'eaire , 30(6):1009–1026, 2013.
• Patricia Bauman, Sean Colbert-Kelly, Jinhae Park, and Daniel Phillips. Liquid Crystal Films with Defects . Ferroelectrics , 431(1):108-120, 2012.
• Patricia Bauman, Jinhae Park, and Daniel Phillips. Analysis of nematic liquid crystals with disclination lines . Arch. Ration. Mech. Anal. , 205(3):795–826, 2012.
• Patricia Bauman and Daniel Phillips. Analysis and stability of bent-core liquid crystal fibers . Discrete Contin. Dyn. Syst. Ser. B , 17(6):1707–1728, 2012.
• Minkyun Kim and Daniel Phillips. Fourfold symmetric solutions to the Ginzburg Landau equation for d-wave superconductors . Comm. Math. Phys. , 310(2):299–328, 2012.
• Sookyung Joo and Daniel Phillips. The phase transitions from chiral nematic toward smectic liquid crystals . Comm. Math. Phys. , 269(2):369–399, 2007.
• Patricia Bauman, Hala Jadallah, and Daniel Phillips. Classical solutions to the time-dependent Ginzburg-Landau equations for a bounded superconducting body in a vacuum . J. Math. Phys. , 46(9):095104, 25, 2005.
• Dan Phillips and Eunjee Shin. On the analysis of a non-isothermal model for superconductivity . European J. Appl. Math. , 15(2):147–179, 2004.
• Nelly Andre, Patricia Bauman, and Dan Phillips. Vortex pinning with bounded fields for the Ginzburg-Landau equation . Ann. Inst. H. Poincar'e Anal. Non Lin'eaire , 20(4):705–729, 2003.
• P. Bauman, D. Phillips, and Q. Shen. Singular limits in polymer-stabilized liquid crystals . Proc. Roy. Soc. Edinburgh Sect. A , 133(1):11–34, 2003.
• P. Bauman, C. Calderer, C. Liu, and D. Phillips. The phase transition between chiral nematic and smectic A∗" role="presentation"> A ∗ A∗ liquid crystals . Arch. Ration. Mech. Anal. , 165(2):161–186, 2002.
• T. Giorgi and D. Phillips. The breakdown of superconductivity due to strong fields for the Ginzburg-Landau model . SIAM Rev. , 44(2):237–256, 2002.
• Daniel Phillips. On one-homogeneous solutions to elliptic systems in two dimensions . C. R. Math. Acad. Sci. Paris , 335(1):39–42, 2002.
• P. Bauman, M. Friesen, and D. Phillips. On the periodic behavior of solutions to a diffusion problem describing currents in a high-temperature superconductor . Phys. D , 137(1-2):172–191, 2000.
• T. Giorgi and D. Phillips. The breakdown of superconductivity due to strong fields for the Ginzburg-Landau model . SIAM J. Math. Anal. , 30(2):341–359, 1999.
• P. Bauman, D. Phillips, and Q. Tang. Stable nucleation for the Ginzburg-Landau system with an applied magnetic field . Arch. Rational Mech. Anal. , 142(1):1–43, 1998.
• Michael M. Dougherty and Daniel Phillips. Higher gradient integrability of equilibria for certain rank-one convex integrals . SIAM J. Math. Anal. , 28(2):270–273, 1997.
• Patricia Bauman, Chao-Nien Chen, and Peter Phillips Daniel and Sternberg. Vortex annihilation in nonlinear heat flow for Ginzburg-Landau systems . European J. Appl. Math. , 6(2):115–126, 1995.
• Daniel Phillips. Remarks on vortices in nonlinear heat flow. Proceedings of Dynamic Systems and Applications, Vol. 1 (Atlanta, GA, 1993) , 283–286, 1994.
• Patricia Bauman and Daniel Phillips. Univalent minimizers of polyconvex functionals in two dimensions . Arch. Rational Mech. Anal. , 126(2):161–181, 1994.
• Patricia Bauman, Neil N. Carlson, and Daniel Phillips. On the zeros of solutions to Ginzburg-Landau type systems . SIAM J. Math. Anal. , 24(5):1283–1293, 1993.
• Patricia Bauman, Nicholas C. Owen, and Daniel Phillips. Maximum principles and a priori estimates for an incompressible material in nonlinear elasticity . Comm. Partial Differential Equations , 17(7-8):1185–1212, 1992.
• Patricia Bauman, Daniel Phillips, and Nicholas C. Owen. Maximal smoothness of solutions to certain Euler-Lagrange equations from nonlinear elasticity . Proc. Roy. Soc. Edinburgh Sect. A , 119(3-4):241–263, 1991.
• Patricia Bauman, Nicholas C. Owen, and Daniel Phillips. Maximum principles and a priori estimates for a class of problems from nonlinear elasticity. Ann. Inst. H. Poincar'e Anal. Non Lin'eaire , 8(2):119–157, 1991.
• Patricia Bauman and Daniel Phillips. A nonconvex variational problem related to change of phase . Appl. Math. Optim. , 21(2):113–138, 1990.
• Daniel Phillips. Existence of solutions of quenching problems . Appl. Anal. , 24(4):253–264, 1987.
• Nicholas D. Alikakos and Daniel Phillips. A remark on positively invariant regions for parabolic systems with an application arising in superconductivity. Quart. Appl. Math. , 45(1):75–80, 1987.
• Patricia Bauman and Daniel Phillips. Large-time behavior of solutions to a scalar conservation law in several space dimensions . Trans. Amer. Math. Soc. , 298(1):401–419, 1986.
• H. W. Alt and D. Phillips. A free boundary problem for semilinear elliptic equations. J. Reine Angew. Math. , 368:63–107, 1986.
• Patricia Bauman and Daniel Phillips. Large-time behavior of solutions to certain quasilinear parabolic equations in several space dimensions . Proc. Amer. Math. Soc. , 96(2):237–240, 1986.
• Michel Langlais and Daniel Phillips. Stabilization of solutions of nonlinear evolution equations. Physical mathematics and nonlinear partial differential equations (Morgantown, W. Va., 1983) , 102:223–228, 1985.
• Michel Langlais and Daniel Phillips. Stabilization of solutions of nonlinear and degenerate evolution equations . Nonlinear Anal. , 9(4):321–333, 1985.
• D. Phillips. The free boundary of a semilinear elliptic equation. Ast'erisque , (118):205–210, 1984.
• Avner Friedman and Daniel Phillips. The free boundary of a semilinear elliptic equation . Trans. Amer. Math. Soc. , 282(1):153–182, 1984.
• D. Phillips. The regularity of solution for a free boundary problem with given homogeneity. Free boundary problems: theory and applications, Vol. I, II (Montecatini, 1981) , 78:682–688, 1983.
• Daniel Phillips. Hausdorff measure estimates of a free boundary for a minimum problem . Comm. Partial Differential Equations , 8(13):1409–1454, 1983.
• Daniel Phillips. A minimization problem and the regularity of solutions in the presence of a free boundary . Indiana Univ. Math. J. , 32(1):1–17, 1983.