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Department of Mathematics Professor Patricia Bauman

Professor Patricia Bauman

Professor Patricia Bauman

Professor Emerita

765-494-1944

MATH 439

baumanp@purdue.edu

Research Interests

  • calculus of variations,
  • partial differential equations,
  • applied mathematics,
  • materials science

My research provides rigorous investigations of the behavior of solutions to systems of partial differential equations that arise in applications of interest. My recent research is on the properties of solutions to systems of nonlinear partial differential equations and energy minimizers for mathematical models developed by physicists to describe liquid crystals and superconductors. In these materials, a rigorous description of the nature of defects is of particular interest.

Publications listed in MathSciNet

(See the CV (PDF) for all publications.)

  1. Bauman, Patricia; Phillips, Daniel. Regularity of minimizers for a general class of constrained energies in two-dimensional domains with applications to liquid crystals. Assoc. Women Math. Ser., 31. Springer, Cham, 2022, 59–78.

  2. Bauman, Patricia; Peng, Guanying. Analysis of minimizers of the Lawrence-Doniach energy for superconductors in applied fields. Discrete Contin. Dyn. Syst. Ser. B 24 (2019), no. 11, 5903–5926.

  3. Bauman, Patricia; Phillips, Daniel; Wang, Changyou. Higher dimensional Ginzburg-Landau equations under weak anchoring boundary conditions. J. Funct. Anal. 276 (2019), no. 2, 447–495.

  4. Bauman, Patricia; Phillips, Daniel. Regularity and the behavior of eigenvalues for minimizers of a constrained Q-tensor energy for liquid crystals. Calc. Var. Partial Differential Equations 55 (2016), no. 4, Art. 81, 22 pp.

  5. Bauman, Patricia; Rubiano, Andrea C. Energy-minimizing nematic elastomers. Discrete Contin. Dyn. Syst. Ser. S 8 (2015), no. 2, 259–282.

  6. Bauman, Patricia; Phillips, Daniel; Park, Jinhae. Existence of solutions to boundary value problems for smectic liquid crystals. Discrete Contin. Dyn. Syst. Ser. S 8 (2015), no. 2, 243–257.

  7. Bauman, Patricia; Park, Jinhae; Phillips, Daniel. Analysis of nematic liquid crystals with disclination lines. Arch. Ration. Mech. Anal. 205 (2012), no. 3, 795–826.

  8. Bauman, Patricia; Phillips, Daniel. Analysis and stability of bent-core liquid crystal fibers. Discrete Contin. Dyn. Syst. Ser. B 17 (2012), no. 6, 1707–1728.

  9. Bauman, Patricia; Ko, Yangsuk. Analysis of solutions to the Lawrence-Doniach system for layered superconductors. SIAM J. Math. Anal. 37 (2005), no. 3, 914–940.

  10. Bauman, Patricia; Jadallah, Hala; Phillips, Daniel. Classical solutions to the time-dependent Ginzburg-Landau equations for a bounded superconducting body in a vacuum. J. Math. Phys. 46 (2005), no. 9, 095104, 25 pp.

  11. Andre, Nelly; Bauman, Patricia; Phillips, Dan. Vortex pinning with bounded fields for the Ginzburg-Landau equation. Ann. Inst. H. Poincaré C Anal. Non Linéaire 20 (2003), no. 4, 705–729.

  12. Bauman, P.; Phillips, D.; Shen, Q. Singular limits in polymer-stabilized liquid crystals. Proc. Roy. Soc. Edinburgh Sect. A 133 (2003), no. 1, 11–34.

  13. Bauman, Patricia; Calderer, M. Carme; Liu, Chun; Phillips, Daniel. The phase transition between chiral nematic and smectic A∗ liquid crystals. Arch. Ration. Mech. Anal. 165 (2002), no. 2, 161–186.

  14. Bauman, Patricia; Marini, Antonella; Nesi, Vincenzo. Univalent solutions of an elliptic system of partial differential equations arising in homogenization. Indiana Univ. Math. J. 50 (2001), no. 2, 747–757.

  15. Bauman, P.; Friesen, M.; Phillips, D. On the periodic behavior of solutions to a diffusion problem describing currents in a high-temperature superconductor. Phys. D 137 (2000), no. 1-2, 172–191.

  16. Bauman, P.; Phillips, D.; Tang, Q. Stable nucleation for the Ginzburg-Landau system with an applied magnetic field. Arch. Rational Mech. Anal. 142 (1998), no. 1, 1–43.

  17. Bauman, Patricia; Chen, Chao-Nien; Phillips, Daniel; Sternberg, Peter. Vortex annihilation in nonlinear heat flow for Ginzburg-Landau systems. European J. Appl. Math. 6 (1995), no. 2, 115–126.

  18. Bauman, Patricia; Phillips, Daniel. Univalent minimizers of polyconvex functionals in two dimensions. Arch. Rational Mech. Anal. 126 (1994), no. 2, 161–181.

  19. Bauman, Patricia; Carlson, Neil N.; Phillips, Daniel. On the zeros of solutions to Ginzburg-Landau type systems. SIAM J. Math. Anal. 24 (1993), no. 5, 1283–1293.

  20. Bauman, Patricia. Qualitative behavior of solutions to a system of partial differential equations from nonlinear elasticity. Lecture Notes in Pure and Appl. Math., 144 Marcel Dekker, Inc., New York, 1993, 53–67.

  21. Bauman, Patricia; Owen, Nicholas C.; Phillips, Daniel. Maximum principles and a priori estimates for an incompressible material in nonlinear elasticity. Comm. Partial Differential Equations 17 (1992), no. 7-8, 1185–1212.

  22. Bauman, Patricia; Phillips, Daniel; Owen, Nicholas C. Maximal smoothness of solutions to certain Euler-Lagrange equations from nonlinear elasticity. Proc. Roy. Soc. Edinburgh Sect. A 119 (1991), no. 3-4, 241–263.

  23. Bauman, Patricia; Owen, Nicholas C.; Phillips, Daniel. Maximum principles and a priori estimates for a class of problems from nonlinear elasticity. Ann. Inst. H. Poincaré C Anal. Non Linéaire 8 (1991), no. 2, 119–157.

  24. Bauman, Patricia; Phillips, Daniel. A nonconvex variational problem related to change of phase. Appl. Math. Optim. 21 (1990), no. 2, 113–138.

  25. Bauman, Patricia. Large-time behavior of solutions to a scalar conservation law in several space dimensions. Contemp. Math., 64. American Mathematical Society, Providence, RI, 1987, 209–217.

  26. Bauman, Patricia; Phillips, Daniel. Large-time behavior of solutions to a scalar conservation law in several space dimensions. Trans. Amer. Math. Soc. 298 (1986), no. 1, 401–419.

  27. Bauman, Patricia; Phillips, Daniel. Large-time behavior of solutions to certain quasilinear parabolic equations in several space dimensions. Proc. Amer. Math. Soc. 96 (1986), no. 2, 237–240.

  28. Bauman, Patricia. A Wiener test for nondivergence structure, second-order elliptic equations. Indiana Univ. Math. J. 34 (1985), no. 4, 825–844.

  29. Bauman, Patricia. Positive solutions of elliptic equations in nondivergence form and their adjoints. Ark. Mat. 22 (1984), no. 2, 153–173.

  30. Bauman, Patricia. Equivalence of the Green's functions for diffusion operators in Rn: a counterexample. Proc. Amer. Math. Soc. 91 (1984), no. 1, 64–68.

  31. Bauman, Patricia. Properties of nonnegative solutions of second-order elliptic equations and their adjoints. ProQuest LLC, Ann Arbor, MI, 1982, 154 pp.