Research interests

Nonlinear partial differential equations   Calculus of variations   Numerical methods for partial differential equations

Problems I have been working on include: Constrained Mountain Pass Algorithm (a numerical method which approximates critical points of a functional under constraints), traveling waves in a suspension bridge or a nonlinearly supported plane, the Fucik spectrum of the Laplace operator, buckling of a thin cylinder, numerical solution of Euler and Navier-Stokes equations.

Selected publications

J. Horak, M. Lucia, A minimax theorem in the presence of unbounded Palais-Smale sequences, Isr. J. Math. 172 (2009), 125-143.   J. Horak, P. J. McKenna, W. Reichel, Very weak solutions with boundary singularities for semilinear elliptic Dirichlet problems in domains with conical corners, J. Math. Anal. Appl. 352 (2009), no. 1, 496-514.   J. Horak, G. J. Lord, M. A. Peletier, Numerical variational methods applied to cylinder buckling, SIAM J. Sci. Comput. 30 (2008), no. 3, 1362-1386.   J. Horak, G. J. Lord, M. A. Peletier, Cylinder buckling: the mountain pass as an organizing center, SIAM J. Appl. Math. 66 (2006), no. 5, 1793-1824.   B. Breuer, J. Horak, P. J. McKenna, M. Plum, A computer-assisted existence and multiplicity proof for travelling waves in a nonlinearly supported beam, J. of Differential Equations 224 (2006), no. 1, 60-97.   J. Horak, Constrained mountain pass algorithm for the numerical solution of semilinear elliptic problems, Numerische Mathematik 98 (2004) 251-276.   R. F. Bass, J. Horak, P. J. McKenna, On the lift-off constant for elastically supported plates, Proc. Amer. Math. Soc. 132 (2004), no. 10, 2951-2958.   J. Horak, W. Reichel, Analytical and numerical results for the Fucik spectrum of the Laplacian, J. Comput. Appl. Math. 161 (2003) 313-338.   J. Horak, P. J. McKenna, Traveling waves in nonlinearly supported beams and plates, Nonlinear Equations: Methods, Models and Applications, Progress in Nonlin. Diff. Eq. Appl., vol. 54, Birkhäuser, Basel 2003, 197-215.   J. Furst, J. Horak, K. Kozel, M. Vavrincova, Modern schemes for computation of transonic flows in internal aerodynamics, Acta Polytechnica (Prague) 40 (2000), no. 4.   M. Fialova, J. Furst, J. Horak, K. Kozel, 2D and 3D transonic flow computation using finite volume method and model of Euler and Navier-Stokes equations, Z. Angew. Math. Mech., 77 (1997), 477-480.