We establish long-time and large-data existence of a weak solution
to the problem describing three-dimensional unsteady flows of an
incompressible fluid, where the viscosity and heat-conductivity
coefficients vary with the temperature. The approach reposes on
considering the equation for the total energy rather than the
equation for the temperature. We consider the spatially periodic
problem.

Eduard Feireisl

Josef Málek

On the Navier-Stokes equations with temperature-dependent transport coefficients

Solutions for a class of nonlinear second-order differential
equations arising in steady Poiseuille flow of an Oldroyd
six-constant model are obtained using the quasilinearization
technique. Existence, uniqueness, and analyticity results are
established using Schauder theory. Numerical results
are presented graphically and salient features of the solutions
are discussed.

F. Talay Akyildiz

K.  Vajravelu

Existence, uniqueness, and quasilinearization results for nonlinear differential equations arising in viscoelastic fluid flow

Dynamics of two coupled periodically driven oscillators is
analyzed via approximate effective equation of motion. The
internal motion is separated off exactly and then approximate
equation of motion is derived. Perturbation analysis of the
effective equation is used to study the dynamics of the initial
dynamical system.

Andrzej  Okni&#324;ski

Jan  Kyzio&#322;

Perturbation analysis of the effective equation for two coupled periodically driven oscillators

This paper deals with the modelling of complex sociopsychological games and reciprocal feelings involving interacting individuals. The modelling is based on suitable developments of the methods of mathematical kinetic theory of active particles with special attention to modelling multiple interactions. A first approach to complexity analysis is proposed referring to both computational and modelling aspects.

Nicola  Bellomo

Bruno  Carbonaro

On the modelling of complex sociopsychological systems with some reasoning about Kate, Jules, and Jim

In classical particle mechanics, it is well understood that while
working with nonholonomic and nonideal constraints, one cannot
expect that the constraint be workless. It is curious that in
continuum mechanics, however, the implications of the result in
classical mechanics have not been clearly understood. In this paper,
we show that in dealing with the response of dissipative systems,
one cannot require that constraints do no work or ignore the fact
that the material response functions depend on the constraint
reaction. An example of this is the viscosity of a fluid depending
on the pressure.

K. R. Rajagopal

Giuseppe Saccomandi

On internal constraints in continuum mechanics

This paper is devoted to the study of the elasticity with porous
dissipation. In the context of the nonlinear problem, we prove
instability and nonexistence of solutions. In the context of the
linear problem, we obtain exponential growth. We also obtain
uniqueness of solutions of the backward in time problem of the
linear equations.

M. C. Leseduarte

R.  Quintanilla

Instability, nonexistence, and uniqueness in elasticity with porous dissipation

About this journal

International Journal of Differential Equations publishes research on differential equations, and related integral equations, from all scientists who use differential equations as tools within their own discipline.

Journal profile

Meet the editorial board

International Journal of Differential Equations maintains an Editorial Board of practicing researchers from around the world, to ensure manuscripts are handled by editors who are experts in the field of study.

Editor spotlight

Submit your proposal

Do you think there is an emerging area of research that really needs to be highlighted? Or an existing research area that has been overlooked or would benefit from deeper investigation? Raise the profile of a research area by leading a Special Issue.

Special Issues

Author guidelines

Editorial board

Databases and indexing

International Journal of Differential Equations - Table of contents

International Journal of Differential Equations | Hindawi

title

International Journal of Differential Equations publishes research on differential equations, and related integral equations, from all scientists who use differential equations as tools within their own discipline.

description

International Journal of Differential Equations

https://images.hindawi.com/journals/ijde/ijde.banner.jpg

International Journal of Differential Equations