相关论文: Stability of periodic solutions of conservation la…

This paper concerns the construction of traveling wave solutions to the free boundary incompressible Navier-Stokes system. We study a single layer of viscous fluid in a strip-like domain that is bounded below by a flat rigid surface and…

In this paper we study existence and stability of shock profiles for a 1-D compressible Euler system in the context of Quantum Hydrodynamic models. The dispersive term is originated by the quantum effects described through the Bohm…

In this note, we report on recent findings concerning the spectral and nonlinear stability of periodic traveling wave solutions of hyperbolic-parabolic systems of balance laws, as applied to the St. Venant equations of shallow water flow…

It is necessary to introduce an external forcing to induce turbulence in a stably stratified fluid. The Heisenberg eddy viscosity technique should in this case suffice to calculate a space-time averaged quantity like the global anisotropy…

We study nonlinear time-asymptotic stability of small--amplitude planar Lax shocks in a model consisting of a system of multi--dimensional conservation laws coupled with an elliptic system. Such a model can be found in context of dynamics…

In the field of differential equations, particularly fluid dynamics, many researchers have shown an interest in the behavior of time periodic solutions. In this paper, we study isentropic gas flow in a bounded interval and apply a time…

This paper is a detailed and self-contained study of the stability properties of periodic traveling wave solutions of the nonlinear Klein-Gordon equation $u_{tt}-u_{xx}+V'(u)=0$, where $u$ is a scalar-valued function of $x$ and $t$, and the…

The manuscript focuses on the theoretical stability analysis of the viscous liquid over a vibrating inclined rigid bed when the fluid undergoes an impact of odd viscosity. Such an impact emerges in the classical fluid owing to the broken…

In this paper we study solitary traveling wave solutions to a damped shallow water system, which is in general quasilinear and of mixed type. We develop a small data well-posedness theory and prove that traveling wave solutions are a…

This paper deals with various cases of resonance, which is a fundamental concept of science and engineering. Specifically, we study the connections between periodic and unbounded solutions for several classes of equations and systems. In…

Ostrovsky's equation with time- and space- dependent forcing is studied. This equation is model for long waves in a rotating fluid with a non-constant depth (topography). A classification of Lie point symmetries and low-order conservation…

This contribution is a follow-up of a recent paper by the authors on adaptive, non-linear time-frequency transforms, focusing on the STFT based transforms. The adaptivity is provided by a focus function, that depends on the analyzed…

We study the existence and stability of periodic traveling-wave solutions for complex modified Korteweg-de Vries equation. We also discuss the problem of uniform continuity of the data-solution mapping.

We give new results concerning the Frobenius integrability and solution of evolution equations admitting travelling wave solutions. In particular, we give a powerful result which explains the extraordinary integrability of some of these…

This article is concerned with the existence of traveling wave solutions, including standing waves, to some models based on configurational forces, describing respectively the diffusionless phase transformations of solid materials, e.g.,…

The Rayleigh-B\'enard instability of the stationary throughflow in a horizontal porous layer, also known as Prats' problem, is here analysed in a fresh new perspective. In fact, the classical analysis of the linear instability, carried out…

A general formulation is presented to derive the equation of motion and to demonstrate thermodynamic consistency for several classes of phase field models at once. It applies to models with a conserved phase field, describing either uniform…

A Hamilton-Jacobi equation with Caputo's time-fractional derivative of order less than one is considered. The notion of a viscosity solution is introduced to prove unique existence of a solution to the initial value problem under periodic…

A study was made of the instability that arises when acoustic and gravity waves propagate in an inhomogeneous medium which is characterized by oscillatory approach of the reaction coordinates to the steady state. It is shown that loss of…

A variational principle for determining unstable periodic orbits of flows as well as unstable spatio-temporally periodic solutions of extended systems is proposed and implemented. An initial loop approximating a periodic solution is evolved…