
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 NavierStokes equations.
Selected publications

J. Horak, M. Lucia,
A minimax theorem in the presence of unbounded
PalaisSmale sequences,
Isr. J. Math. 172 (2009), 125143.


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, 496514.


J. Horak, G. J. Lord, M. A. Peletier,
Numerical variational methods applied to cylinder buckling,
SIAM J. Sci. Comput. 30 (2008), no. 3, 13621386.


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, 17931824.


B. Breuer, J. Horak, P. J. McKenna,
M. Plum, A computerassisted existence and multiplicity
proof for travelling waves in a nonlinearly supported
beam, J. of Differential Equations 224 (2006), no. 1,
6097. 

J. Horak, Constrained
mountain pass algorithm for the numerical solution
of semilinear elliptic problems, Numerische
Mathematik 98 (2004) 251276. 

R. F. Bass, J. Horak, P. J. McKenna,
On the liftoff constant for elastically supported plates,
Proc. Amer. Math. Soc. 132 (2004), no. 10, 29512958. 

J. Horak, W. Reichel,
Analytical and numerical results for the Fucik
spectrum of the Laplacian,
J. Comput. Appl. Math. 161 (2003) 313338. 

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,
197215. 

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 NavierStokes equations,
Z. Angew. Math. Mech., 77 (1997), 477480. 




