Preprints

Published Articles

    48. On the inverse spectral problem for Euclidean triangles
          Proc. Royal Soc. A Math. Phys. Eng. Sci. 467 (2011), 1546-1562 (with Pedro Antunes).

    47. A spectral Bernstein theorem
          Ann. Mat. Pura Appl. 190 (2011), 77-90 (with Isabel Salavessa ).

    46. Bounds for the first Dirichlet eigenvalue of triangles and quadrilaterals
          ESAIM: Control, Optimisation and Calculus of Variations 16 (2010), 646-676 (with Bartlomjej Siudeja).

    45. On the characterization of harmonic and subharmonic functions via mean-value properties
          Potential Anal. 32 (2010), 189-200 (with João Palhoto Matos).

    44. Asymptotics of Dirichlet eigenvalues and eigenfunctions of the Laplacian on thin domains in Rd
          J. Funct. Anal. 258 (2010), 893-912 (with Denis Borisov).

    43. On the effect of sharp rises in blood pressure in the Shah-Humphrey model for intracranial saccular aneurysms
          Biomech. Model. Mechanobiology 8 (2009), 457-471.

    42. Eigenvalue asymptotics, inverse problems and a trace formula for the linear damped wave equation
          J. Differential Equations 247 (2009), 3028-3039 (with Denis Borisov).

    41. Singular asymptotic expansions for Dirichlet eigenvalues and eigenfunctions on thin planar domains
          Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009), 547-560 (with Denis Borisov).

    39. A sharp upper bound for the first Dirichlet eigenvalue and the growth of the isoperimetric constant of convex domains
          Proc. Amer. Math. Soc. 136 (2008), 2997-3006 (with David Krejcirik).

    38. Location of the nodal set for thin curved tubes
          Indiana Univ. Math. J. 57 (2008), 343-376 (with David Krejcirik).

    37. A numerical study of the spectral gap
          J. Phys. A 41 (2008), 055201 (with Pedro Antunes).

    35. Precise bounds and asymptotics for the first Dirichlet eigenvalue of triangles and rhombi
          J. Funct. Anal. 251 (2007), 376-398.

    34. Unbounded planar domains whose second nodal line does not touch the boundary
          Math. Res. Lett. 14 (2007), 107-111
    (with David Krejcirik).

    33. Waveguides with combined Dirichlet and Robin boundary conditions
          Math. Phys. Anal. Geom. 9 (2006), 335-352
    (with David Krejcirik).

    32. New bounds for the principal Dirichlet eigenvalue of planar regions
          Experiment. Math. 15 (2006), 333-342
    (with Pedro Antunes).

    31. A Li-type criterion for zero-free half-planes of Riemann's zeta function
          J. London Math. Soc. 73 (2006), 399-414.

    30. Upper and lower bounds for the first Dirichlet eigenvalue of a triangle
          Proc. Amer. Math. Soc.
    134 (2006), 2083-2089.

    29. Extension of Abel's Lemma with q-series implications
          Ramanujan J. 10 (2005), 137-152 (with
    George E. Andrews).

    28. Geometrically induced discrete spectrum in curved tubes
          Differential Geom. Appl. 23 (2005), 95-105
    (with Boris Chenaud,
    Pierre Duclos and David Krejcirik).

    27. Integrals of polylogarithmic functions, recurrence relations, and associated Euler sums
          Math. Comp. 74 (2005), 1425-1440.

    26. Instability results for the damped wave equation in unbounded domains
          J. Differential Equations 211 (2005), 168-186
    (with
    David Krejcirik).

    25. On the first twisted Dirichlet eigenvalue
          Comm. Anal. Geom. 12 (2004), 1083-1103
    (with
    Antoine Henrot).

    24. A lower bound to the spectral threshold in curved tubes
          R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci. 460 (2004), 3457-3467
    (with
    Pavel Exner and David Krejcirik).

    23. Closed nodal lines and interior hot spots of the second eigenfunction of the Laplacian on surfaces
          Indiana Univ. Math. J. 51 (2002), 305-316.

    22. Memory driven instability in a diffusion process
          SIAM J. Math. Anal. 33 (2002), 1090-1106
    (with Brian R. Duffy and
    Michael Grinfeld).

    21. On the invariant spectrum of S1-invariant metrics on S2
          Proc. London Math. Soc. 84 (2002), 213-230
    (with
    Miguel Abreu).

    20. On minimal eigenvalues of Schrödinger operators on manifolds
          Commun. Math. Phys. 217 (2001), 375-382.

    19. Lyapunov functionals and stability for FitzHugh-Nagumo systems
          J. Differential Equations 169 (2001), 208-227 (with
    Carlos Rocha).

    18. Delay induced instabilities in gyroscopic systems
          SIAM J. Control Optimization 39 (2000), 196-207.

    17. Stability of stationary solutions of nonlocal reaction-diffusion equations in n-dimensional space
          Differential and Integral Equations 13 (2000), 265-288 (with Mikhail Vishnevskii).

    16. Spectral sequences for quadratic pencils and the inverse spectral problem for the damped wave equation
          J. Math. Pures Appl.
    78 (1999), 965-980.


    15. On the optimal value of the spectral abscissa for a system of linear oscillators
          SIAM J. Matrix Anal. Appl. 21 (1999), 195-208 (with
    Peter Lancaster).

    14. Optimizing the rate of decay of solutions of the wave equation using genetic algorithms: a counterexample to the constant damping conjecture
          SIAM J. Control Optimization 37 (1999), 376-387.

    13. Quadratic matrix polynomials with Hamiltonian spectrum and oscillatory damped systems
          Z. Angew. Math. Phys. 50 (1999), 64-81.

    12. Nonlocal reaction-diffusion equations
          Differential Equations with Applications to Biology 187-204, Fields Inst. Commun. 21, Am. Math. Soc. 1999.

    11. Positivity results for a nonlocal elliptic equation
          Proc. Roy. Soc. Edinburgh 128 (1998), 697-715 (with
    Guido Sweers).

    10. The linear wave equation, Hamiltonian symmetry, and the importance of being odd
          Disc. Cont. Dyn. Syst. 4 (1998), 635-640.

      9. Eigenvalue problems for the wave equation with strong damping
          Proc. Roy. Soc. Edinburgh A 127 (1997), 755-771.

      8. Stability of finite-dimensional systems with indefinite damping
          Adv. Math. Sci. Appl.
    7 (1997), 435-446 (with
    Michael Grinfeld and Philip Knight).

      7. Some results on the stability and bifurcation of stationary solutions of delay-diffusion equations
          J. Math. Anal. Appl.
    206 (1997), 59-82.


      6. Stability results for the wave equation with indefinite damping
          J. Differential Equations 132 (1996), 338-352 (with
    Enrique Zuazua).

      5. On some eigenvalue problems related to the wave equation with indefinite damping
          J. Differential Equations
    127 (1996), 320-335.


      4. Stability of stationary solutions of a nonlocal reaction-diffusion equation
          Quart. J. Mech. Appl. Math. 48 (1995), 557-582.

      3. Stationary solutions of an equation modelling ohmic heating
          Appl. Math. Lett.
    7 (1994), 1-6 (with
    Michael Grinfeld).

      2. Bifurcation and stability of stationary solutions of nonlocal scalar reaction-diffusion equations
          J. Dynam. Differential Equations 6 (1994), 613-629.

      1. A nonlocal Sturm-Liouville eigenvalue problem
          Proc. Roy. Soc. Edinburgh A 124 (1994), 169-188.

Books (as editor)

Proceedings

      3. Characterization and Parameterization of the Singular Manifold of a Simple 6–6 Stewart Platform
         Nonlinear Science and Complexity (2011), 255-262, J.A.T. Machado et al. eds.
    (with Tiago Charters).

      2. (In)stability results for the wave equation with indefinite damping
         Proceedings of Equadiff 95 (1998), 350-355

      1. Bogdanov singularity in the FitzHugh-Nagumo equations
         Proceedings of Equadiff 91 (1993), 496-500 (with Carlos Rocha).

Reports

    10. Asymptotic behaviour of some eigenvalue optimisation problems
         Oberwolfach report no. 33/2012.

      8. Detecting singularities of Stewart platforms
         Mathematics-in-Industry Case Studies 1 (2009), 66-80 Fields Institute Publications (with Tiago Charters and Ricardo Enguiça).

      6. Approximating low eigenvalues of the Laplacian: analysis, geometry and numerics
         Oberwolfach report no. 06/2009.

      1. Sharp dynamic bounds for eigenvalues of the Laplacian
         Oberwolfach report no. 18/2007.

Other