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Václav Klika

Associate Professor
Dept. of Mathematics
FNSPE, CTU in Prague


My main interests are – apart from my family – good reads, sports, and research. Regarding the last one, I consider myself as an applied mathematician with major interests in modelling in general, including the way how to formulate thermodynamically consistent models (non-equilibrium thermodynamics provides a means for such formulations; CIT, EIT, GENERIC) and how to analyse them (stability, symmetries of DEs, asymptotic methods), and the emergence of spatial organisation (diffusion-driven instability and beyond). Topics that attracted my attention up to now include non-equilibrium thermodynamics in general, (self-organisation) pattern formation, coupling phenomena, mixture theory, bone remodelling, cartilage, PEM membranes, or simple swimmers in Stokes flow. My research is described in higher detail below and can be followed on researchgate.

Equations of mathematical physics (RMF)

The theory of generalised functions and its usage to solve linear PDEs. Integral equations, Fredholm operators, and their counterparts in elliptic PDEs (Sturm-Liouville theory, orthonormal basis).

Introduction to semigroup theory (TPG)

Qualitative properties of solutions to abstract Cauchy problems in Banach spaces. The suitability of semigroup properties for wellposedness, various continuities of semigroups, Hille-Yosida theorem, Lumer-Philips theorem, types of solutions to the abstract Cauchy problem, spectral mapping theorem and its relation to Lyapunov stability.

Mathematical Biology (MBI)

Illustration of the learned mathematical tools to study qualitative properties of models inspired from population dynamics or biology, including discrete, continuous, and spatial models. Tools revealing key long-time behaviour include the identification of fixed points and their stability, periodic solutions and their stability, Poincare maps, asymptotics and we also venture briefly into non-equilibrium thermodynamics to gain some understanding of model formulations.

Calculus (ANB3, ANB4)

A rather standard course on the foundations of mathematical analysis.

New possible projects for student's

Vážení studenti, trochu podrobnější popis možných studentských témat ve spolupráci se mnou naleznete zde.

Non-equilibrium thermodynamics

There are many possible avenues here: boundary conditions in mixtures, biphasic and binary mixture model, functional constraints as an extension of Onsager-Casimir reciprocal relations, transport models beyond Fick or Stefan-Maxwell, symmetric hyperbolicity of models..

Self-organisation (pattern formation)

Although there has been a rapid development of this field, there are still many open problems including: the effect of growing domains, natural wave speed of pattern, nondiffusibles and their role in stratified systems, hyperbolic models of reaction-diffusion phenomena, thermodynamically consistent models such as the recent Burger's type model

Modelling of various physical phenomena

My approach to model formulation always stems from non-equilibrium thermodynamics but then the potential applications are accordingly wide and include: biomechanics (cartilage, bone), mechanochemical coupling, transport phenomena in PEM fuel cells, upscaled PNP equations as a replacement of Donnan theory,...


(office 107a)
Trojanova 13
120 00 Prague 2
Czech Republic

vaclav.klika (at)

+420 22435 8545


Sep 2001 - Jun 2006

Master's degree in Applied Mathematics at FNSPE, CTU in Prague

MSc, CTU in Prague

Oct 2006 - Oct 2009

Doctoral degree in Applied Mathematics at FNSPE, CTU in Prague

PhD, CTU in Prague

Jan 2004 - Dec 2015

researcher in Institute of Thermomechanics, Czech Academy of Sciences

research scientist

Mar 2010 - Oct 2016

Applied Mathematics, Dept. Mathematics, FNSPE, CTU in Prague

Assist. prof.

Oct 2016 -

Applied Mathematics, Dept. Mathematics, FNSPE, CTU in Prague

Assoc. prof.



Maths Institute (Oxford, UK), Isaac Newton Institute (Cambridge, UK), ETH, Ecole Polytechnique (Montreal), University of Zaragoza (Zaragoza)

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