We review the class of implicit algebraic constitutive relations for fluids which includes in its
ambit those whose material properties depend on the invariants of the stress, the symmetric …

In the first part of the paper we provide a new classification of incompressible fluids
characterized by a continuous monotone relation between the velocity gradient and the …

Many real fluids exhibit response characteristics that cannot be satisfactorily described by
the classical Navier–Stokes fluid model and such fluids are referred to as non-Newtonian …

Recent advances in the development of implicit constitutive relations to describe the
response of both solids and fluids have greatly increased the repertoire of the modeler in his …

The chapter starts with overview of the derivation of the balance equations for mass,
momentum, angular momentum and total energy, which is followed by a detailed discussion …

In order to understand nonlinear responses of materials to external stimuli of different sort,
be they of mechanical, thermal, electrical, magnetic, or of optical nature, it is useful to have at …

We study a general class of nonlinear elliptic problems associated with the differential
inclusion β (x, u)− div (a (x,∇ u)+ F (u))∋ f, where f∈ L1 (Ω). The vector field a (⋅,⋅) is …

We consider a generalization of the Kelvin-Voigt model where the elastic part of the Cauchy
stress depends non-linearly on the linearized strain and the dissipative part of the Cauchy …

We will present the proof of existence of renormalized solutions to a nonlinear parabolic
problem∂ tu− div a (⋅, D u)= f with right-hand side f and initial data u 0 in L 1. The growth …

Our studies are directed to the existence of weak solutions to a parabolic problem containing
a multi-valued term. The problem is formulated in the language of maximal monotone …