Keywords:
- $\infty$-Laplacian
- Algebraic turbulence model
- Almost everywhere convergence of gradients
- Analytical solutions
- Anelastic approximation
- a~priori bounded gradient
- Blood vessel
- boundary regularity
- bounded divergence of the velocity
- Capillarity stress tensor
- Cauchy problem
- Cauchy stress
- Compressible fluid
- Compressible fluids
- compressible fluid
- Compressible Navier-Stokes-Fourier system
- constitutive relations
- Convective term
- Couette flow
- Cylindrical Couette flow
- Darcy–Forchheimer equation
- Density gradient
- Dirichlet and Neumann boundary conditions
- discontinuous flux
- discontinuous viscosity
- elasto-plasticity
- electrorheological fluids
- Entropy solution
- existence
- Existence of solution
- existence result for large data
- Existence theory
- Galerkin scheme
- Generalized Navier-Stokes fluid
- Generalized Navier-Stokes-Fourier system
- generalized Newtonian fluids
- Global existence
- global--in--time existence
- global-in-time existence
- Granular materials
- Hagen–Poiseuille flow
- Hausdorf measure
- Heat conducting fluid
- Heat flux
- Helmholtz potential
- Hyperbolic scalar conservation laws
- implicit constitutive equation
- implicit constitutive relations
- Implicit constitutive theory
- Incompressible fluid
- Incompressible fluids
- Incompressible non-Newtonian fluid
- inhomogeneous Euler fluid
- Inhomogeneous fluid
- Internal energy
- Johnson-Segalman
- Kelvin-Voigt model
- Korteweg fluid
- Korteweg stress
- Korteweg tensor
- large data
- large data existence
- Large deformation
- Lipschitz approximation of a Bochner function
- Lipschitz approximations of Sobolev functions
- Lipschitz truncation
- local-in-time well-posedness
- Long-time existence
- Low Froude number
- Low Mach number
- low Mach number limit
- Lyapunov function
- Maximal monotone graph
- Maximization and rate of entropy production
- Maximum/minimum principle
- Mixture
- Navier-Stokes-Fourier equations
- Navier’s slip boundary condition
- Navier’s slip boundary conditions
- Navier–Stokes equations
- Newtonian fluids
- Non-linear convection–diffusion equation
- Non-linear heat equation
- non-linear wave equation
- non-Newtonian fluid
- nonlinear parabolic equation
- nonlinear parabolic systems
- Normal stress differences
- numerical simulation
- Oberbeck-Boussinesq ap- proximation
- Optimal shape design
- Outflow boundary condition
- Paper machine headbox
- Poiseuille flow
- positive density.
- power law fluid
- Power-law fluid
- Power-law fluids
- Pressure dependent material coefficient
- pressure dependent viscosity
- Pressure-dependent viscosity
- Rate of dissipation
- Rate type fluid
- regularity
- renormalized solution
- Rheology
- Rothe approximation
- shear rate dependent viscosity
- shear-dependent viscosity
- Singular limits
- singular set
- smooth solution
- spatially periodic problem
- stability
- Stokes-Fourier system
- stress diffusion
- Stress power
- Stress power-law fluids
- stress-diffusion
- suitable weak solution
- temperature dependent viscosity
- temperature-dependent viscosity
- the viscosity increasing with a scalar quantity
- thermodynamics
- time discretization
- times of blow-up
- turbulent kinetic energy model
- uniqueness
- unsteady flows
- viscoelastic fluid
- viscoelastic fluids
- viscoelastic heat-conducting fluids
- viscoelastic solid
- weak solution
- weak solutions
- Young measures
- \\ temperature-dependent material moduli
Publications of Málek, Josef
2021
| , and , Global weak solution of the diffusive Johnson-Segalman model of a viscoelastic heat-conducting fluid, 2021 |
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| , and , Large data existence theory for three-dimensional unsteady flows of rate-type viscoelastic fluids with stress diffusion (2021), in: Advances in Nonlinear Analysis, 10:1(501--521) |
[DOI] |
| , and , On evolutionary problems with a-priori bounded gradients, 2021 |
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| , , and , On incompressible heat-conducting viscoelastic rate-type fluids with stress-diffusion and purely spherical elastic response (2021), in: SIAM J. Math. Anal., 53:4(3985--4030) |
[DOI] |
| , and , On nonlinear problems of parabolic type with implicit constitutive equations involving flux (2021), in: Math. Models Methods Appl. Sci., 31:10(2039--2090) |
[DOI] |
| , , and , On planar flows of viscoelastic fluids of Burgers type, 2021 |
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| , , , and , On unsteady flows of pore pressure-activated granular materials (2021), in: Z. Angew. Math. Phys., 70:1(Paper No. 6) |
[DOI] |
2020
| , , and , A simple construction of a thermodynamically consistent mathematical model for non-isothermal flows of dilute compressible polymeric fluids (2020), in: Fluids, 5:3(133) |
[DOI] |
2019
| , , and , Numerical scheme for simulation of transient flows of non-newtonian fluids characterised by a non-monotone relation between the symmetric part of the velocity gradient and the Cauchy stress tensor (2019), in: Acta Mechanica, 230:3(729-747) |
[DOI] |
| , and , On a class of compressible viscoelastic rate-type fluids with stress--diffusion (2019), in: Nonlinearity, 32:12(4665--4681) |
[DOI] |
| , and , Thermodynamics and stability of non-equilibrium steady states in open systems (2019), in: Entropy, 21:7(704) |
[DOI] |
| , , and , Three-dimensional flows of pore pressure-activated Bingham fluids (2019), in: Mathematical Models and Methods in Applied Sciences, 29:11(2089-2125) |
[DOI] [URL] |
2018
| , and , Derivation of the variants of the Burgers model using a thermodynamic approach and appealing to the concept of evolving natural configurations (2018), in: Fluids, 3:4 |
[DOI] [URL] |
| , and , Numerical simulations of an incompressible piezoviscous fluid flowing in a plane slider bearing (2018), in: Meccanica, 53:1-2(209--228) |
[DOI] |
| , , and , Thermodynamics of viscoelastic rate-type fluids with stress diffusion (2018), in: Physics of Fluids, 30:2 |
[DOI] |
2017
| , , and , A continuum model of heterogeneous catalysis: thermodynamic framework for multicomponent bulk and surface phenomena coupled by sorption (2017), in: International Journal of Engineering Science |
| , , and , A novel view on computations of steady flows of Bingham fluids using implicit constitutive relations (2017), in: Journal of Non-Newtonian Fluid Mechanics |
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| , , , and , Determination of pressure data from velocity data with a view towards its application in cardiovascular mechanics. Part 2: a study of aortic valve stenosis. (2017), in: International Journal of Engineering Science |
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| and , Internal flows of incompressible fluids subject to stick-slip boundary conditions (2017), in: Vietnam Journal of Mathematics, 45(2017--220) |
[DOI] |
| , , and , On the existence of integrable solutions to nonlinear elliptic systems and variational problems with linear growth (2017), in: Archive for Rational Mechanics and Analysis, 225:2(717--769) |
[DOI] [URL] |
| , , and , PDE analysis of a class of thermodynamically compatible viscoelastic rate-type fluids with stress-diffusion (2017), in: Contemporary Mathematics, American Mathematical Society |
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2016
| , and , A thermodynamically compatible model for describing asphalt binders: solutions of problems (2016), in: International Journal of Pavement Engineering, 17:6(550-564) |
[DOI] |
| and , Derivation of Equations for Continuum Mechanics and Thermodynamics of Fluids, in: Handbook of Mathematical Analysis in Mechanics of Viscous Fluids, Springer International Publishing, 2016 |
[DOI] |
| , , , and , Determination of pressure data from velocity data with a view toward its application in cardiovascular mechanics. Part 1. Theoretical considerations (2016), in: International Journal of Engineering Science, 105(108 - 127) |
[DOI] [URL] |
| , and , On PDE analysis of flows of quasi-incompressible fluids (2016), in: Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM), 96:4(491–508) |
[DOI] |
| , and , On power-law fluids with the power-law index proportional to the pressure (2016), in: Applied Mathematics Letters, 62(118--123) |
[DOI] |
| and , On Unsteady Internal Flows of Bingham Fluids Subject to Threshold Slip on the Impermeable Boundary, in: Recent Developments of Mathematical Fluid Mechanics, pages 135--156, Birkhauser, 2016 |
[DOI] |
| , and , Response of a class of mechanical oscillators described by a novel system of differential-algebraic equations (2016), in: Applications of Mathematics, 61:1(79--102) |
[DOI] |
2015
| , and , A generalization of the Darcy-Forchheimer equation involving an implicit, pressure-dependent relation between the drag force and the velocity (2015), in: Journal of Mathematical Analysis and Applications, 424:1(785-801) |
[DOI] |
| , and , A thermodynamically compatible model for describing the response of asphalt binders (2015), in: International Journal of Pavement Engineering, 16:4(297-314) |
[DOI] |
| , and , Analysis and approximation of a strain-limiting nonlinear elastic model (2015), in: Mathematics and Mechanics of Solids, 20:1(92–118) |
[DOI] |
| , , and , Existence of solutions for the anti-plane stress for a new class of "strain-limiting" elastic bodies (2015), in: Calculus of Variations and PDE's, 54:2(2115--2147) |
[DOI] |
| , and , Global weak solutions to a class of non-Newtonian compressible fluids (2015), in: Math. Methods Appl. Sci., 38:16(3482–3494) |
[DOI] |
| , and , On a variant of the Maxwell and Oldroyd-B models within the context of a thermodynamic basis (2015), in: International Journal of Non-Linear Mechanics, 76(42--47) |
[DOI] |
| , and , On generalized Stokes' and Brinkman's equations with pressure- and shear-dependent viscosity and drag coefficient (2015), in: Nonlinear Anal. Real World Appl., 26(109--132) |
[DOI] |
| and , Preconditioning and the Conjugate Gradient Method in the Context of Solving PDEs, SIAM, SIAM Spotlight Series, 2015 |
[URL] |
2014
| , , and , On elastic solids with limiting small strain: modelling and analysis (2014), in: EMS Surveys in Mathematical Sciences, 1:2(283–332) |
[DOI] |
| , , and , On the natural structure of thermodynamic potentials and fluxes in the theory of chemically non-reacting binary mixtures (2014), in: Acta Mechanica, 225:11(3157-3186) |
[DOI] |
| , and , On the Regularity of Two-Dimensional Unsteady Flows of Heat-Conducting Generalized Newtonian Fluids (2014), in: Nonlinear Analysis: Real World Applications, 19(89--104) |
[DOI] |
2013
| , and , Existence of Global Weak Solutions to Implicitly Constituted Kinetic Models of Incompressible Homogeneous Dilute Polymers (2013), in: Communications in Partial Differential Equations, 58:5(882--924) |
[DOI] |
2012
| , , , and , A Thermodynamically Compatible Rate Type Fluid to Describe the Response of Asphalt (2012), in: Mathematics and Computers in Simulation, 82:10(1853--1873) |
[DOI] [URL] |
| , , , and , On flows of fluids described by an implicit constitutive equation characterized by a maximal monotone graph, in: Mathematical Aspects of Fluid Mechanics, pages 23--51, Cambridge University Press, 2012 |
[URL] |
| , and , On Kelvin-Voigt model and its generalizations (2012), in: Evolution Equations and Control Theory, 1:1(17-42) |
[DOI] [URL] |
| , and , On the Development and Generalizations of Allen-Cahn and Stefan Equations within a Thermodynamic Framework (2012), in: ZAMP - Zeitschrift für Angewandte Mathematik und Physik(1--18) |
[DOI] [URL] |
| , and , On the development and generalizations of Cahn-Hilliard equations within a thermodynamic framework (2012), in: ZAMP - Zeitschrift für Angewandte Mathematik und Physik, 63:1(145-169) |
[DOI] |
| , , and , On Unsteady Flows of Implicitly Constituted Incompressible Fluids (2012), in: SIAM J. Math. Anal., 44:4(2756--2801) |
[DOI] |
2011
| , and , An $L^2$-maximal regularity result for the evolutionary Stokes-Fourier system (2011), in: Applicable Analysis, 90:1(31--45) |
[DOI] [URL] |
| , , and , Further remarks on simple flows of fluids with pressure dependent viscosities (2011), in: Nonlinear Analysis: Real World Applications, 12:1(394-402) |
[DOI] [URL] |
| , and , On evolutionary Navier-Stokes-Fourier type systems in three spatial dimensions (2011), in: Comment. Math. Univ. Carolin., 52:1(89--114) |
[URL] |
| , and , On Hausdorff Dimension of Blow-Up Times Relevant to Weak Solution of Generalized Navier-Stokes Fluids, pages 116--129, Gakuto International Series, Mathematical Sciences and Applications, volume 35, 2011 |
[URL] |
| , , and , On scalar hyperbolic laws with discontinuous flux (2011), in: Mathematical Models and Methods in Applied Sciences, 21:1(89--113) |
[DOI] [URL] |
| , and , On solvability of a non-linear heat equation with a non-integrable convective term and data involving measures (2011), in: Nonlinear Analysis: Real World Applications, 12:1(571--591) |
[DOI] [URL] |
| , and , On The Need For Compatibility Of Thermal And Mechanical Data In Flow Problems (2011), in: International Journal of Engineering Science, 49:7(537--543) |
[DOI] [URL] |
2010
| and , Compressible Generalized Newtonian Fluids (2010), in: ZAMP - Zeitschrift für Angewandte Mathematik und Physik, 61:6(1097-1110) |
[DOI] [URL] |
| , and , Generalizations of the Navier--Stokes fluid from a new perspective (2010), in: International Journal of Engineering Science, 48:12(1907-1924) |
[DOI] [URL] |
| , and , Large Data Existence Result for Unsteady Flows of Inhomogeneous Shear-Thickening Heat-Conducting Incompressible Fluids (2010), in: Communications in Partial Differential Equations, 35:10(1891-1919) |
[DOI] [URL] |
| and , On compressible Korteweg fluid-like materials (2010), in: International Journal of Engineering Science, 48:11(1313--1324) |
[DOI] [URL] |
| , , and , On the Modelling of the Synovial Fluid (2010), in: Advances in Tribology, 2010(1--12) |
[DOI] [URL] |
| , , and , On the motion of incompressible inhomogeneous Euler-Korteweg fluids (2010), in: Discrete and Continuous Dynamical Systems - Series S, 3:3(497-515) |
[DOI] [URL] |
| , and , Stress concentration due to an elliptic hole in a degrading linearized elastic solid (2010), in: International Journal of Applied Mechanics and Engineering, 15:1(35-49) |
| , and , Unsteady flows of fluids with pressure dependent viscosity in unbounded domains (2010), in: Nonlinear Analysis: Real World Applications, 11:5(3968-3983) |
[DOI] |
2009
| , and , A Navier-Stokes-Fourier system for incompressible fluids with temperature dependent material coefficients (2009), in: Nonlinear Analysis: Real World Applications, 10:2(992--1015) |
[DOI] [URL] |
| , and , Analysis of the flows of incompressible fluids with pressure dependent viscosity fulfilling {$\nu(p,\cdot)\to+\infty$} as {$p\to+\infty$} (2009), in: Czechoslovak Math. J., 59(134):2(503--528) |
[DOI] [URL] |
| , and , Mathematical analysis of unsteady flows of fluids with pressure, shear-rate, and temperature dependent material moduli that slip at solid boundaries (2009), in: SIAM J. Math. Anal., 41:2(665--707) |
[DOI] [URL] |
| , and , Mathematical Results Concerning the Unsteady Flows of Chemically Reacting Incompressible Fluids, chapter 2, pages 26--53, Cambridge University Press, London Mathematical Society Lecture Note Series, volume 364, 2009 |
[URL] |
| , and , On boundary regularity for the stress in problems of linearized elasto-plasticity (2009), in: International Journal of Advances in Engineering Sciences and Applied Mathematics, 1:4(141-156) |
[DOI] [URL] |
| , , and , On steady flows of incompressible fluids with implicit power-law-like rheology (2009), in: Advances in Calculus of Variations, 2:2(109--136) |
[DOI] [URL] |
| , , and , Shape Optimization for Navier-Stokes Equations with Algebraic Turbulence Model: Existence Analysis (2009), in: Applied Mathematics and Optimization, 60:2(185-212) |
[DOI] [URL] |
2008
| and , A thermodynamic framework for a mixture of two liquids (2008), in: Nonlinear Anal. Real World Appl., 9:4(1649--1660) |
[DOI] |
| , , and , Anelastic approximation as a singular limit of the compressible Navier-Stokes system (2008), in: Communications in Partial Differential Equations, 33:1-3(157--176) |
[DOI] [URL] |
| , , and , Flows of incompressible fluids subject to Navier's slip on the boundary (2008), in: Computers & Mathematics with Applications, 56:8(2128--2143) |
[DOI] [URL] |
| , Mathematical properties of flows of incompressible power-law-like fluids that are described by implicit constitutive relations (2008), in: Electron. Trans. Numer. Anal., 31(110--125) |
[URL] |
| , and , Navier´s slip and incompressible limits in domains with variable bottoms (2008), in: Discrete and Continuous Dynamical Systems - Series S, 1:3(427-460) |
[DOI] [URL] |
| , and , On Lipschitz truncations of Sobolev functions (with variable exponent) and their selected applications (2008), in: ESAIM Control Optim. Calc. Var., 14:2(211--232) |
[DOI] |
2007
| , and , An existence result for the shape optimization problem governed by Navier-Stokes equations with algebraic turbulence model, 2007 |
[URL] |
| and , Incompressible rate type fluids with pressure and shear-rate dependent material moduli (2007), in: Nonlinear Anal. Real World Appl., 8:1(156--164) |
[DOI] |
| , and , Navier's slip and evolutionary Navier-Stokes-like systems with pressure and shear-rate dependent viscosity (2007), in: Indiana Univ. Math. J., 56:1(51--85) |
[DOI] |
| , and , On flows of an incompressible fluid with a discontinuous power-law-like rheology (2007), in: Comput. Math. Appl., 53:3-4(531--546) |
[DOI] |
2006
| and , Mathematical properties of the equations governing the flow of fluids with pressure and shear rate dependent viscosities, chapter 7, pages 407--444, Elsevier B. V., Handbook of Mathematical Fluid Dynamics, volume 4, 2006 |
[DOI] [URL] |
| and , On the modeling of inhomogeneous incompressible fluid-like bodies (2006), in: Mechanics of Materials, 38(233-242) |
[DOI] |
| and , On the Navier-Stokes equations with temperature-dependent transport coefficients (2006), in: Differ. Equ. Nonlinear Mech.(Art. ID 90616, 14 pp. (electronic)) |