Dr. Patricia Bauman
Professor Emerita- MATH 439
Research Interest(s):
partial differential equations, applied mathematics
Professional Research
My research is on systems of nonlinear elliptic & parabolic partial differential equations with applications to materials. I am currently investigating properties of solutions to systems
that describe liquid crystals in two or three dimensions, including the the nature of defects in these materials
MA34100-SPRING 2019 COURSE PAGE
Courses
MA 341:
- Sec. 042, CRN 60863, 1:30-2:20,
- Sec. 041, CRN 22122, 2:30-3:20
Office Hours
Office Hours for Spring 2020: Math 718, times to be announced
Selected Publications
- Patricia Bauman and Guanying Peng. Analysis of minimizers of the Lawrence-Doniach energy for superconductors in applied fields. Discrete Contin. Dyn. Syst. Ser. B , 24(11):5903–5926, 2019.
- 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.
- 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.
- Patricia Bauman and Andrea C. Rubiano. Energy-minimizing nematic elastomers . Discrete Contin. Dyn. Syst. Ser. S , 8(2):259–282, 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.
- 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.
- Patricia Bauman and Yangsuk Ko. Analysis of solutions to the Lawrence-Doniach system for layered superconductors . SIAM J. Math. Anal. , 37(3):914–940, 2005.
- 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.
- 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.
- Patricia Bauman, M. Carme Calderer, and Daniel Liu Chun and Phillips. The phase transition between chiral nematic and smectic \romanA∗" role="presentation"> \roman A ∗ \romanA∗ liquid crystals . Arch. Ration. Mech. Anal. , 165(2):161–186, 2002.
- Patricia Bauman, Antonella Marini, and Vincenzo Nesi. Univalent solutions of an elliptic system of partial differential equations arising in homogenization . Indiana Univ. Math. J. , 50(2):747–757, 2001.
- 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.
- 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.
- 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.
- 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. Qualitative behavior of solutions to a system of partial differential equations from nonlinear elasticity. Geometric analysis and nonlinear partial differential equations (Denton, TX, 1990) , 144:53–67, 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.
- Patricia Bauman. Large-time behavior of solutions to a scalar conservation law in several space dimensions . The legacy of Sonya Kovalevskaya (Cambridge, Mass., and Amherst, Mass., 1985) , 64:209–217, 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.
- 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.
- Patricia Bauman. A Wiener test for nondivergence structure, second-order elliptic equations . Indiana Univ. Math. J. , 34(4):825–844, 1985.
- Patricia Bauman. Positive solutions of elliptic equations in nondivergence form and their adjoints . Ark. Mat. , 22(2):153–173, 1984.
- Patricia Bauman. Equivalence of the Green's functions for diffusion operators in Rn" role="presentation"> R n Rn : a counterexample . Proc. Amer. Math. Soc. , 91(1):64–68, 1984.
- Patricia Ellen Bauman. PROPERTIES OF NONNEGATIVE SOLUTIONS OF SECOND-ORDER ELLIPTIC EQUATIONS AND THEIR ADJOINTS . , 154, 1982.