Curtis Holliman Headshot

Department

  • Mathematics

    • School

  • School of Arts and Sciences

    • Research Interests:

    My current interests lie in nonlinear partial differential equations, in particular those that model various aspects of fluid dynamics.  I mainly use tools that come from harmonic/Fourier analysis to examine various aspects of the well-posedness of these equations.

     

    Publications:

    1. C. Holliman & L. Hyslop, Well-posedness for a modified nonlinear Schrödinger equation modeling the formation of rogue waves, Open Journal of Mathematical Analysis, Vol. 5 (2021), Issue 1, 105– 117.
    2. A. Himonas & C. Holliman, Non-uniqueness for the Fokas-Olver-Rosenau-Qiao equation, Journal of Mathematical Analysis and Applications (2019), 470 (1), 647–658.
    3.  A. Himonas, C. Holliman & C. Kenig Construction of 2-peakon Solutions and Ill-Posedness for the Novikov equation, SIAM Journal on Mathematical Analysis (2018), 50 (3), 2968–3006.
    4. A. Himonas, K. Grayshan & C. Holliman Ill-Posedness for the b-Family of Equations, Journal of Nonlinear Science (2016), 26 (5), 1175–1190.
    5. A. Himonas, C. Holliman & K. Grayshan Norm inflation and ill-posedness for the Degasperis- Procesi equation, Communications in Partial Differential Equations (2014), 39 (12), 2198–2215.
    6. A. Himonas & C. Holliman The Cauchy problem for a generalized Camassa-Holm equation, Ad- vances in Differential Equations (2014), 19 (1/2), 161–200.
    7. J. Gorsky, A. Himonas, C. Holliman & G. Petronilho, The Cauchy problem of a periodic higher order KdV equation in analytic Gevrey spaces, J. Math. Anal. Appl. 405 (2013), no. 2, 349–361.
    8. A. Himonas & C. Holliman The Cauchy problem for the Novikov equation, Nonlinearity 25 (2012), no. 2, 449–479.
    9. A. Himonas and C. Holliman, On the Well-Posedness of the Degasperis-Procesi Equation, Dis- crete Contin. Dyn. Syst. 31, (2011), 469–488.
    10. C. Holliman, Non-Uniform Dependence and Well-Posedness for the Periodic Hunter-Saxton Equation, J. Diff. Int. Eq. 23, No. 11-12, (2010), 1159–1194.

    Undergraduate Research:

    One of my activities involves engaging undergraduate students in mathematical research.  I have had funded research assistantships for students to study problems ranging from the modeling of crime, disease transmission and wave collisions in fluids.