Viscoelastic Cahn–Hilliard models for tumor growth
We introduce a new phase field model for tumor growth where viscoelastic effects are taken
into account. The model is derived from basic thermodynamical principles and consists of a …
into account. The model is derived from basic thermodynamical principles and consists of a …
[HTML][HTML] Large data existence theory for three-dimensional unsteady flows of rate-type viscoelastic fluids with stress diffusion
We prove that there exists a weak solution to a system governing an unsteady flow of a
viscoelastic fluid in three dimensions, for arbitrarily large time interval and data. The fluid is …
viscoelastic fluid in three dimensions, for arbitrarily large time interval and data. The fluid is …
Optimal time-decay estimates for an Oldroyd-B model with zero viscosity
J Huang, Y Wang, H Wen, R Zi - Journal of Differential Equations, 2022 - Elsevier
In this work, we consider the Cauchy problem for a diffusive Oldroyd-B model in three
dimensions. Some optimal time-decay rates of the solutions are derived via analysis of …
dimensions. Some optimal time-decay rates of the solutions are derived via analysis of …
Global existence and decay rates of solutions to the Oldroyd-B model with stress tensor diffusion
J Huang, Q Liu, R Zi - Journal of Differential Equations, 2024 - Elsevier
In this paper, we consider the Oldroyd-B model with stress tensor diffusion in R d with d≥ 2.
We first establish the global well-posedness of solutions to this model for small initial data (u …
We first establish the global well-posedness of solutions to this model for small initial data (u …
Simulating structured fluids with tensorial viscoelasticity
We consider an immersed elastic body that is actively driven through a structured fluid by a
motor or an external force. The behavior of such a system generally cannot be solved …
motor or an external force. The behavior of such a system generally cannot be solved …
Cross-diffusion waves in hydro-poro-mechanics
We propose a new class of wave-phenomena in multiphase solids (and granular media)
triggered by Hydro-Poro-Mechanical coupling and cross-diffusion feedbacks of porous …
triggered by Hydro-Poro-Mechanical coupling and cross-diffusion feedbacks of porous …
[HTML][HTML] Thermodynamics and stability of non-equilibrium steady states in open systems
Thermodynamical arguments are known to be useful in the construction of physically
motivated Lyapunov functionals for nonlinear stability analysis of spatially homogeneous …
motivated Lyapunov functionals for nonlinear stability analysis of spatially homogeneous …
Quasistatic hypoplasticity at large strains Eulerian
T Roubíček - Journal of Nonlinear Science, 2022 - Springer
The isothermal quasistatic (ie acceleration neglected) hardening-free plasticity at large
strains is considered, based on the standard multiplicative decomposition of the total strain …
strains is considered, based on the standard multiplicative decomposition of the total strain …
Non-convex dissipation potentials in multiscale non-equilibrium thermodynamics
Reformulating constitutive relation in terms of gradient dynamics (being derivative of a
dissipation potential) brings additional information on stability, metastability and instability of …
dissipation potential) brings additional information on stability, metastability and instability of …
Some gradient theories in linear visco-elastodynamics towards dispersion and attenuation of waves in relation to large-strain models
T Roubíček - Acta Mechanica, 2024 - Springer
Various spatial-gradient extensions of standard viscoelastic rheologies of the Kelvin–Voigt,
Maxwell's, and Jeffreys' types are analysed in linear one-dimensional situations as far as the …
Maxwell's, and Jeffreys' types are analysed in linear one-dimensional situations as far as the …