Research

Research interest

Integrodifferential equations
Integral models for viscoelastic fluids
Evolution equations
Lojasiewicz gradient inequality
Semigroup theory

Publications

Preprints

T. Bárta, P. Davis, P. Kaplický, Maximal regularity of Stokes problem with dynamic boundary condition --- Hilbert setting, preprint 2024.
T. Bárta, Convergence to equilibrium for second order integrodifferential equations with polynomially decaying kernels, preprint 2018.
T. Bárta, Sharp and optimal decay estimates for solutions of gradient-like systems, preprint 2017.

Published

T. Bárta, J. Horáček, Calculation of resonances by analytical continuation: role of asymptotic behavior of coupling function, Physica scripta 95 (2020), no. 6.
T. Bárta, Exact rate of decay for solutions to damped second order ODE's with a degenerate potential, Evol. Equ. Control Theory 7 (2018), no. 4, 531-543.
T. Bárta, Optimal decay estimates for solutions to damped second order ODE's, Electron. J. Qual. Theory Differ. Equ. 2018, No. 36, 1-9.
T. Bárta, Rate of convergence to equilibrium and Lojasiewicz-type estimates, J. Dyn. Diff. Equat. 29 (2017), no. 4, 1553-1568.
T. Bárta, Decay estimates for solutions of an abstract wave equation with general damping function, Electron. J. Differential Equations, Vol. 2016 (2016), No. 334, pp. 1-17.
T. Bárta, E. Fašangová, Convergence to equilibrium for solutions of an abstract wave equation with general damping function, J. Diff. Equ. 260, no. 3, 2016, 2259 – 2274.
T. Bárta, V. Janeček, D. Pražák, Heat conduction problem of an evaporating liquid wedge, Electron. J. Diff. Equ., Vol. 2015 (2015), No. 53, 1 - 18.
T. Bárta, Global existence for a nonlinear model of 1D chemically reacting viscoelastic body, Riv. Mat. Univ. Parma 5, no. 2, 2014, 399 - 423.
T. Bárta, One-dimensional model describing the non-linear viscoelastic response of materials, Comment. Math. Univ. Carolin. 55, no. 2, 2014, 227 – 246.
T. Bárta, Convergence to equilibrium of relatively compact solutions to evolution equations, Electron. J. Diff. Equ., Vol. 2014 (2014), No. 81, 1 - 9.
V. Janeček, B. Andreotti, D. Pražák, T. Bárta a V. S. Nikolayev, Moving contact line of a volatile fluid, Phys. Rev. E 88, 060404, 2013
T. Bárta, Global existence for a system of nonlocal PDEs with applications to chemically reacting incompressible fluids, Cent. Eur. J. Math. 11(6), 2013, 1112 - 1128
T. Bárta, Global existence for an Oldroyd-type model for viscoelastic fluids, Riv. Mat. Univ. Parma 4, no. 1, 2013, 37 - 54
T. Bárta, Nonmonotone nonconvolution functions of positive type and applications, Comment.Math.Univ.Carolin. 53, no. 2, 2012, 211 - 220.
T. Bárta, R. Chill, E. Fašangová, Every ordinary differential equation with a strict Lyapunov function is a gradient system, Monatsh. Math. 166, No. 1, 2012, 57 - 72.
T. Bárta, Delayed quasilinear evolution equations with application in heat flow, Math. Nachr. 283, No. 5, 2010, 648 – 658.
T. Bárta, Two notes on eventually differentiable families of operators, Comment.Math.Univ.Carolin. 51, vol. 1, 2010, 19-24.
T. Bárta, Delayed quasilinear evolution equations with BV-coefficients, Z. Anal. ihre Anwend. 29, 2010, 149--162.
T. Bárta, A generation theorem for hyperbolic equations with coefficients of bounded variation in time Riv.Mat.Univ.Parma (7) 9, 2008, 17--30.
T. Bárta, Smooth solutions of Volterra equations via semigroups, Bull. Austral. Math. Soc. 78, 2008, 249 - 260.
T. Bárta, Polynomial decay for solutions of hyperbolic integrodifferential equations, Glasgow Math. J. 50, 2008, 575 - 581.
T. Bárta, On R-sectorial derivatives on Bergman spaces, Bull. Austral. Math. Soc. 77, 2008, 305 - 313.
T. Bárta, Analytic solutions of Volterra equations via semigroups, Semigroup Forum 76, no. 1, 2008, 142 - 148.
T. Bárta, Integrodifferential Equations in Banach Spaces, Ph.D. Thesis, Charles University of Prague, 2005
T. Bárta, Laplace Transform and Semigroup Approach to Integrodifferential Equations, Riv. Mat. Univ. Parma (7) 3, 2004, pp. 1 - 17
T. Bárta, Asymptotic behaviour of Volterra integrodifferential equations, Tuebinger Berichte 10, 2001, pp. 9 - 18.
T. Bárta, Asymptotic behaviour of Volterra integrodifferential equations, Diploma thesis, Charles University of Prague, 2001.
P. Pyrih, T. Bárta, D. Opěla, P. Růžička, R. Šámal, Irreducible mapping and the lightness of open mappings, Southwest J. Pure Appl. Math., 2001, no. 2, 30 - 42.
P. Pyrih, T. Bárta, D. Opěla, R. Šámal, Irreducible mappings and HU-terminal continua, Southwest J. Pure Appl. Math. 1999, no. 2, 31 - 41.
P. Pyrih, T. Bárta, D. Opěla, R. Šámal, A continuum where absolute terminality and HU-terminality coincide, Questions Answers Gen. Topology 17, 1999, no. 2, 233 – 235.