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Stability of hydrodynamic model for semiconductor

Massimiliano Daniele Rosini (2005)

Archivum Mathematicum

In this paper we study the stability of transonic strong shock solutions of the steady state one-dimensional unipolar hydrodynamic model for semiconductors in the isentropic case. The approach is based on the construction of a pseudo-local symmetrizer and on the paradifferential calculus with parameters, which combines the work of Bony-Meyer and the introduction of a large parameter.

Stability of oscillating boundary layers in rotating fluids

Nader Masmoudi, Frédéric Rousset (2008)

Annales scientifiques de l'École Normale Supérieure

We prove the linear and non-linear stability of oscillating Ekman boundary layers for rotating fluids in the so-called ill-prepared case under a spectral hypothesis. Here, we deal with the case where the viscosity and the Rossby number are both equal to ε . This study generalizes the study of [23] where a smallness condition was imposed and the study of [26] where the well-prepared case was treated.

Stability of periodic stationary solutions of scalar conservation laws with space-periodic flux

Anne-Laure Dalibard (2011)

Journal of the European Mathematical Society

This article investigates the long-time behaviour of parabolic scalar conservation laws of the type ∂ t u + div y A ( y , u ) - Δ y u = 0 , where y ∈ ℝ N and the flux A is periodic in y . More specifically, we consider the case when the initial data is an L 1 disturbance of a stationary periodic solution. We show, under polynomial growth assumptions on the flux, that the difference between u and the stationary solution behaves in L 1 norm like a self-similar profile for large times. The proof uses a time and space change of variables which is...

Stability of periodic waves in Hamiltonian PDEs

Sylvie Benzoni-Gavage, Pascal Noble, L. Miguel Rodrigues (2013)

Journées Équations aux dérivées partielles

Partial differential equations endowed with a Hamiltonian structure, like the Korteweg–de Vries equation and many other more or less classical models, are known to admit rich families of periodic travelling waves. The stability theory for these waves is still in its infancy though. The issue has been tackled by various means. Of course, it is always possible to address stability from the spectral point of view. However, the link with nonlinear stability  - in fact, orbital stability, since we are...

Stability of vibrations for some Kirchhoff equation with dissipation

Prasanta Kumar Nandi, Ganesh Chandra Gorain, Samarjit Kar (2014)

Applications of Mathematics

In this paper we consider the boundary value problem of some nonlinear Kirchhoff-type equation with dissipation. We also estimate the total energy of the system over any time interval [ 0 , T ] with a tolerance level γ . The amplitude of such vibrations is bounded subject to some restrictions on the uncertain disturbing force f . After constructing suitable Lyapunov functional, uniform decay of solutions is established by means of an exponential energy decay estimate when the uncertain disturbances are insignificant....

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