相关论文: Stability of equilibrium solutions of a double pow…

The linear stability of two exact stationary solutions of the parametrically driven, damped nonlinear Dirac equation is investigated. Stability is ascertained through the resolution of the eigenvalue problem, which stems from the…

We study the steady uniphase and multiphase solutions of the discretized nonlinear damped wave equation.Conditions for the stability abd instability of the steady solutions are given;in the instability case the linear stable and unstable…

We consider some reaction-diffusion equations describing systems with the nonlocal consumption of resources and the intraspecific competition. Sharp conditions on the coefficients are obtained to ensure the stability and instability of…

This paper analyzes the stability of a reactiondiffusion equation coupled with a finite-dimensional controller through Dirichlet boundary input and Neumann boundary output. Going against the flow, we intend to propose numerical certificates…

A general system of several ordinary differential equations coupled with a reaction-diffusion equation in a bounded domain with zero-flux boundary condition is studied in the context of pattern formation. These initial-boundary value…

We analyze the static response to perturbations of nonequilibrium steady states that can be modeled as one-dimensional diffusions on the circle. We demonstrate that an arbitrary perturbation can be broken up into a combination of three…

We study the stability of reaction-diffusion equations in presence of noise. The relationship of stability of solutions between the stochastic ordinary different equations and the corresponding stochastic reaction-diffusion equation is…

A general system of n ordinary differential equations coupled with one reaction-diffusion equation, considered in a bounded N-dimensional domain, with no-flux boundary condition is studied in a context of pattern formation. Such initial…

We investigate the stability of the equilibrium-induced optimal value in one-dimensional diffusion setting for a time-inconsistent stopping problem under non-exponential discounting. We show that the optimal value is semi-continuous with…

Reaction-diffusion equations coupled to ordinary differential equations (ODEs) may exhibit spatially low-regular stationary solutions. This work provides a comprehensive theory of asymptotic stability of bounded, discontinuous or…

We study reaction-diffusion equations in cylinders with possibly nonlinear diffusion and possibly nonlinear Neumann boundary conditions. We provide a geometric Poincar\'e-type inequality and classification results for stable solutions, and…

In this paper, we study the local behaviour of solutions near the fixed points of a reaction-diffusion equation with discontinuous nonlinearity. By employing an appropriate linearization around the fixed points, which involves the Dirac…

We study the planar front solution for a class of reaction diffusion equations in multidimensional space in the case when the essential spectrum of the linearization in the direction of the front touches the imaginary axis. At the linear…

In this paper we study a convection-reaction-diffusion equation of the form \begin{equation*} u_t=\varepsilon(h(u)u_x)_x-f(u)_x+f'(u), \quad t>0, \end{equation*} with a nonlinear diffusion in a bounded interval of the real line. In…

We consider the stability of a system of equations which are a singular perturbation of the incompressible rigid-plastic flow equations used to model granular flow. A linear stability analysis shows that solutions of these equations are…

An asymptotic method for finding instabilities of arbitrary $d$-dimensional large-amplitude patterns in a wide class of reaction-diffusion systems is presented. The complete stability analysis of 2- and 3-dimensional localized patterns is…

We consider positive one-dimensional solutions of a Lane-Emden relative Dirichlet problem in a cylinder and study their stability/instability properties as the energy varies with respect to domain perturbations. This depends on the exponent…

The linear stability of stratified two-phase flows in rectangular ducts is studied numerically. The linear stability analysis takes into account all possible infinitesimal three-dimensional disturbances and is carried out by solution of the…

This work studies the instability of stochastic scalar reaction diffusion equations, driven by a multiplicative noise that is white in time and smooth in space, near to zero, which is assumed to be a fixed point for the equation. We prove…

We analyze the pattern forming ability and pattern stability for a one-dimensional non-linear transport-diffusion equation on the circle. We show that the trivial steady state is stable when diffusion is sufficiently strong. In the limit…