相关论文: Time-periodic boundary effects on the shocks for s…
This paper is concerned with the stability of stationary solutions of the conservation law $\partial_t u + \mathrm{div}_y A(y,u) -\Delta_y u=0$, where the flux $A$ is periodic with respect to its first variable. Essentially two kinds of…
We consider the compressible barotropic Navier-Stokes equations in a half-line and study the time-asymptotic behavior toward the outgoing viscous shock wave. Precisely, we consider the two boundary problems: impermeable wall and inflow…
In this paper, the asymptotic-time behavior of solutions to an initial boundary value problem in the half space for 1-D isentropic Navier-Stokes system is investigated. It is shown that the viscous shock wave is stable for an impermeable…
We consider the temporal periodic solutions to general nonhomogeneous quasilinear hyperbolic equations with a kind of weak diagonal dominant structure. Under the temporal periodic boundary conditions, the existence, stability and uniqueness…
This paper is concerned with the time-asymptotic behavior of strong solutions to an initial-boundary value problem of the compressible Navier-Stokes-Korteweg system on the half line $\mathbb{R}^+$. The asymptotic profile of the problem is…
In order to understand the nonlinear stability of many types of time-periodic travelling waves on unbounded domains, one must overcome two main difficulties: the presence of embedded neutral eigenvalues and the time-dependence of the…
Thermal instabilities can cause a radiative shock to oscillate, thereby modulating the emission from the post-shock region. The mode frequencies are approximately quantised in analogy to those of a vibrating pipe. The stability properties…
The stability of solutions under periodic perturbations for both inviscid and viscous conservation laws is an interesting and important problem. In this paper, a large-amplitude viscous shock under space-periodic perturbation for the…
Extending investigations of M\'etivier&Zumbrun in the hyperbolic case, we treat stability of viscous shock and boundary layers for viscous perturbations of multidimensional hyperbolic systems with characteristics of variable multiplicity,…
This paper is concerned with the boundary-value problem on the Boltzmann equation in bounded domains with diffuse-reflection boundary where the boundary temperature is time-periodic. We establish the existence of time-periodic solutions…
In many occurrences of fluid-structure interaction time-periodic motions are observed. We consider the interaction between a fluid driven by the three dimensional Navier-Stokes equation and a two dimensional linearized elastic Koiter shell…
In this paper, we investigate the asymptotic behavior of solutions to the Cauchy problem for the scalar viscous conservation law where the far field states are prescribed. Especially, we deal with the case when the viscosity is of…
We prove the large-time asymptotic orbital stability of strictly entropic Riemann shock solutions of first order scalar hyperbolic balance laws, under piecewise regular perturbations provided that the source term is dissipative about…
We demonstrate that it is possible to control a normal transonic shock to move periodically by adjusting the boundary conditions at the entrance or the exit of the tube, for which, the phenomena has been observed in engineering. In this…
We establish nonlinear stability and asymptotic behavior of traveling periodic waves of viscous conservation laws under localized perturbations or nonlocalized perturbations asymptotic to constant shifts in phase, showing that long-time…
This paper discusses new perspectives and approaches to the problem of disk dynamics where, in this study, we focus on the effects of viscous instabilities influenced by boundary effects. The Boussinesq approximation of the viscous large…
We study the large-time asymptotic stability of viscous shock profile to the outflow problem of barotropic Navier-Stokes equations on a half line. We consider the case when the far-field state as a right-end state of 2-Hugoniot shock curve…
This paper shows that for the three-dimensional compressible isentropic Navier-Stokes equations, the planar viscous shocks are time-asymptotically stable to suitably small initial perturbations with zero masses. In particular, the…
This paper is concerned with the global existence and stability of solution to the quasi linear hyperbolic-parabolic chemotaxis system on the half-line,which was proposed in[1] to primarily describe the formation of coherent vascular…
This thesis is concerned with dynamics of conservative nonlinear waves on bounded domains. In general, there are two scenarios of evolution. Either the solution behaves in an oscillatory, quasiperiodic manner or the nonlinear effects cause…