相关论文: Pointwise Green function bounds and stability of c…

In this paper, we study the orbital stability for a four-parameter family of periodic stationary traveling wave solutions to the generalized Korteweg-de Vries equation. In particular, we derive sufficient conditions for such a solution to…

Stability of the traveling wave solution to a general class of one-dimensional nonlocal evolution equations is studied in $L^2$-spaces, thereby providing an alternative approach to the usual spectral analysis with respect to the supremum…

This paper is concerned with the study of the nonlinear stability of the contact discontinuity of the Navier-Stokes-Poisson system with free boundary in the case where the electron background density satisfies an analogue of the Boltzmann…

Many-body quantum-mechanical stationary states that have real valued wavefunctions are shown to satisfy a classical conservation of energy equation with a kinetic energy function. The terms in the equation depend on the probability…

In this paper, we determine spectral stability results of periodic waves for the critical Korteweg-de Vries and Gardner equations. For the first equation, we show that both positive and zero mean periodic traveling wave solutions possess a…

In this paper, we present a series of applications of the pointwise estimates of the (unrestricted) Green tensor of the nonstationary Stokes system in the half space, established in our previous work [CMP 2023]. First, we show the…

We obtain geometric insight into the stability of traveling pulses for reaction-diffusion equations with skew-gradient structure. For such systems, a Maslov index of the traveling wave can be defined and related to the eigenvalue equation…

For homogeneous and isotropic linearly elastic solids and for incompressible fluids under low-Reynolds-number conditions the fundamental solutions of the associated continuum equations were derived a long time ago for bulk systems. That is,…

Guided by molecular dynamics simulations, we generalize the Navier-Stokes-Fourier constitutive equations and the continuum motion equations to include both transverse and longitudinal temperatures. To do so we partition the contributions of…

We describe recent analytical and numerical results on stability and behavior of viscous and inviscid detonation waves obtained by dynamical systems/Evans function techniques like those used to study shock and reaction diffusion waves. In…

We derive and justify a new effective model for a compressible viscous liquid-vapor flow on a spray-like scale, i.e., for settings with a large number of phase boundaries. As a model on the detailed scale, we start from a parabolic…

We give an exhaustive, non-perturbative classification of exact travelling-wave solutions of a perturbed sine-Gordon equation (on the real line or on the circle) which is used to describe the Josephson effect in the theory of…

We extend the result on the stability of travelling waves for stochastic Nagumo equations in [St] to general bistable reaction-diffusion equations with both additive and multiplicative noise, using a variational approach based on functional…

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…

We establish long-time stability of multi-dimensional noncharacteristic boundary layers of a class of hyperbolic--parabolic systems including the compressible Navier--Stokes equations with inflow [outflow] boundary conditions, under the…

In this paper, the large time behavior of the solutions for the Cauchy problem to the one-dimensional compressible Navier-Stokes system with the motion of a viscous heat-conducting perfect polytropic gas is investigated.Our result shows…

We consider the non-isentropic compressible Navier-Stokes equation in a perturbed half space with an outflow boundary condition as well as the supersonic condition. This equation models a compressible viscous, heat-conductive, and Newtonian…

Edges are abundant when elastic solids glide in guiding rails or fluids are contained in vessels. We here address induced displacements in elastic solids or small-scale flows in viscous fluids in the vicinity of one such edge. For this…

The pointwise space-time behavior of the Green's function of the three-dimensional relativistic Boltzmann equation is studied in this paper. It is shown that the Green's function has a decomposition of the macroscopic diffusive waves and…

So far existence of dissipative weak solutions for the compressible Navier-Stokes equations (i.e. weak solutions satisfying the relative energy inequality) is known only in the case of boundary conditions with non zero inflow/outflow (i.e.,…