Continuum mechanics with dislocations, with the Cattaneo-type heat conduction, with mass
transfer, and with electromagnetic fields is put into the Hamiltonian form and into the form of …

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 …

The field of aeroacoustics has gained much attention since the well-known acoustic
analogies were first published in the 1950s. In parallel, the continuous growth of …

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 …

While the assumption of the “no-slip” condition at a solid boundary is unquestioningly
applied to study the flow characteristics of a Navier–Stokes fluid, there was considerable …

We propose thermodynamically consistent models for viscoelastic fluids with a stress
diffusion term. In particular, we derive variants of compressible/incompressible …

We derive a model describing the evolution of a nematic liquid–crystal material under the
action of thermal effects. The first and second laws of thermodynamics lead to an extension …

Viscoelastic rate-type fluid models involving the stress and frame-indifferent time derivatives
of second order, like those in Burgers' model, are used to describe the complicated …

We derive a class of thermodynamically consistent variants of Maxwell/Oldroyd-B type
models for incompressible viscoelastic fluids. In particular, we study the models that allow …

In this work, we present a phase-field model for tumour growth, where a diffuse interface
separates a tumour from the surrounding host tissue. In our model, we consider transport …