Marianna Ruggieri

Exact solutions for a nonlinear model of dissipative media

Group classification of a mathematical model describing one-dimensional motion in nonlinear dissipative medium is performed. Reduced equations through the optimal system of subalgebras are obtained and some exact solutions are shown.

Approximate symmetries in nonlinear viscoelastic media

Approximate symmetries of a mathematical model describing one-dimensional motion in a medium with a small nonlinear viscosity are studied. In a physical application, the approximate solution is calculated making use of the approximate generator of the first-order approximate symmetry.MSC:35J25, 32A37, 43A15, 35A58, 42B20.

Similarity reduction and closed form solutions for a model derived from two-layer fluids

In this paper, we study an integrable system of coupled KdV equations, derived by Gear and Grimshaw (Stud. Appl. Math. 70(3):235-258, 1984), modeling the strong interaction of two-dimensional, long, internal gravity waves propagating on neighboring pycnoclines in a stratified fluid. In particular, we present the complete group classification of the model and find conditions on arbitrary parameters for which the system admits symmetries. Some exact solutions of physical relevance are derived.

Symmetries and reduction techniques for dissipative models

Symmetries and reduction techniques are applied to a mathematical model describing one-dimensional motions in nonlinear dissipative media. Reduced equations through the optimal system of subalgebras are performed and some exact invariant solutions are shown in a physical application.

Extended thermodynamics revisited : renormalized flux variables and second sound in rigid solids

Propagation of heat waves in rigid bodies is investigated. The originality of the approach is that it rests on a revisited version of extended irreversible thermodynamics. In comparison with earlier developments, two innovations are proposed. First, we depart from the linear approach, best illustrated by Cattaneos relation, to explore the non-linear regime. Second, the extra variables are no longer the usual dissipative fluxes, but renormalized expressions of the fluxes, in order to include the specific material properties of the systems under study. The present model is particularly well suited for studying heat transport at low temperatures in dielectric crystals.

Kink Solutions for a Class of Generalized Dissipative Equations

We study, in this paper, a generalized viscoelastic equation which includes several interesting models considered in some recent papers. Many physically important nonlinear PDEs can be reduced to nonlinear ODEs by means of reduction techniques. So it is significant and very interesting to study, among all the closed-form solutions admitted by the model, the corresponding kink waves. A plot of the obtained solution is performed.

Conservation laws for a model derived from two layer-fluids

In this paper, using a recent approach for finding conservation laws, based on Lie symmetries, we establish the conservation laws for a model admitting quasi self-adjoint equations.

New exact solutions for a coupled KdV-like model

An extension of a recent method is applied in order to construct new explicit exact solutions for a system of coupled KdV-like equations.

On a hierarchy of traveling wave solutions in a shallow stratified fluid

An algebraic method is applied to construct a complete hierarchy of traveling wave solutions for a system of coupled KdV-like equations.

Analytical and numerical solutions of fractional type advection-diffusion equation

In this paper, the case of an equation involving fractional derivatives with respect to a single independent variable has been analyzed. Our aim is to determine its Lie’s symmetry, and by using them, obtain analytical and numerical solutions.