TEACHING


PUBLICATIONS AND PREPRINTS
  1. Refined blow-up results for nonlinear fourth order differential equations
    Communications on Pure and Applied Analysis, vol. 14, no. 2, 677-693 (2015).
    Joint with: Filippo Gazzola.
  2. A lower bound for the amplitude of traveling waves of suspension bridges
    Nonlinear Analysis, vol. 75, no. 13, 5212-5214 (2012).
    Joint with: John G. Stalker.
  3. Asymptotic expansion of radial solutions for supercritical biharmonic equations
    Nonlinear Differential Equations and Applications, vol. 19, no. 4, 401-415 (2012).
  4. Dispersion relation for water waves with non-constant vorticity
    European Journal of Mechanics B/Fluids, vol. 34, 7-12 (2012).
  5. Qualitative behavior of global solutions to some nonlinear fourth order differential equations
    Journal of Differential Equations, vol. 251, no. 10, 2696-2727 (2011).
    Joint with: Elvise Berchio, Alberto Ferrero and Filippo Gazzola.
  6. The existence of ground states for fourth-order wave equations
    Nonlinear Analysis, vol. 73, no. 2, 367-373 (2010).
    Joint with: P. Joseph McKenna.
  7. Stability and intersection properties of solutions to the nonlinear biharmonic equation
    Nonlinearity, vol. 22, no. 7, 1653-1661 (2009).
  8. Supercritical biharmonic equations with power-type nonlinearity
    Annali di Matematica Pura ed Applicata, vol. 188, no. 1, 171-185 (2009).
    Joint with: Alberto Ferrero and Hans-Christoph Grunau.
  9. Sharp bounds on 2m/r for static spherical objects
    Classical and Quantum Gravity, vol. 25, no. 19, 195021 (2008).
    Joint with: John G. Stalker.
  10. Instability of steady states for nonlinear wave and heat equations
    Journal of Differential Equations, vol. 241, no. 1, 184-205 (2007).
    Joint with: Walter A. Strauss.
  11. On the asymptotic behavior of nonlinear waves in the presence of a short-range potential
    Manuscripta Mathematica, vol. 119, no. 3, 323-345 (2006).
    Joint with: Kimitoshi Tsutaya.
  12. Small-data scattering for nonlinear waves of critical decay in two space dimensions
    Differential and Integral Equations, vol. 19, no. 6, 601-626 (2006).
    Joint with: Kimitoshi Tsutaya.
  13. Small-data scattering for nonlinear waves with potential and initial data of critical decay
    Discrete and Continuous Dynamical Systems, vol. 16, no. 1, 87-106 (2006).
  14. Existence and blow up of small-amplitude nonlinear waves with a sign-changing potential
    Journal of Differential Equations, vol. 219, no. 2, 259-305 (2005).


CONTACT INFORMATION

Address: School of Mathematics, Trinity College, Dublin 2, IRELAND
Office: Hamilton Building, Room 20.32c
Phone: 353-1-896-3946
Fax: 353-1-896-2282
E-mail: pete@maths.tcd.ie