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 R.S. 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 R.S. 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 R.S. 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
    David Krejcirik).

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


      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).


    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.